B737-800 Captain reported landing safely after inflight shutdown of the left engine following the loss of oil pressure and quantity.

Narrative

The flight was delayed initially by over an hour due to multiple aircraft swaps. Ultimately the aircraft which we were assigned arrived to the gate with an open Maintenance write up requiring oil to be added to the left engine. The left engine arrived with 11 quarts of oil just one day after previously needing oil with a documented level of 11 QTS. The flight departed normally and the climb out and cruise phase were ordinary. We descended and cruised at flight level 210 in order to achieve a smooth ride. Just prior to the top of descent the lower display unit auto populated the engine instrumentation that had been hidden; in compliance with company en route procedures. There was a shock effect with the realization that the auto populated engine data was displaying low oil pressure between 14 and 18 psi and oil quantity of zero. The FO (First Officer) noticed it first and said 'your aircraft'. I replied 'my aircraft' and evaluated what had just been presented to us. Despite the shock effect; we promptly ran the engine low oil pressure checklist; and the low oil quantity checklist; which both led to a precautionary engine shut down checklist. While reducing the thrust levers for the descent; and also to comply with the engine shut down checklist; there was a momentary flash of red on the oil pressure indication. We requested priority handling with ATC and stated our souls on board and fuel in hours and minutes. The First Officer who was the pilot monitoring completed all the checklists. The approach briefing had already been completed while in cruise flight. The precautionary engine shut down occurred approximately 100 miles south of ZZZ. The surface winds in the region were reported to be 310@31G48 just prior to this event occurring. Based upon the runway alignments of ZZZ1; ZZZ2 and ZZZ3 relative to the wind; I made the command authority decision to continue to ZZZ as that was deemed by me to be the closest most suitable airport given our situation. By the grace of God; the winds diminished at our time of arrival such that they were 310@23G36; which is still not insignificant. Due to our close proximity to ZZZ while the First Officer was conducting the one engine in operative; landing checklist I called back to the cabin to notify the flight attendants of a precautionary landing; and to not be surprised to see ARFF (Airport Rescue and Firefighting) equipment approach the aircraft after landing; and that the left engine had to be shut down. I notified the passengers with a short PA informing them that one of the engines was not cooperating properly and had to be shut down; but that the aircraft was performing well and that we would be landing shortly in ZZZ and that as is normal in a situation like this to expect to see safety vehicles approach the aircraft after we land. The First Officer caught me back up with her status on the checklist progress and continued to the non-routine landing checklist. Dispatch was notified via ACARS 7700 code of our status and destination. During the descent; both thrust levers had been at idle with the auto throttle disengaged; and the descent mode selected had been VNAV. We requested a vector to intercept the localizer to Runway XXL. When we selected in the FMC a course extension; the VNAV command switched from VNAV SPD to VNAV PATH and the aircraft rate of descent substantially slowed; causing the aircraft speed to slow and my reaction to increase thrust on the right engine was delayed; causing the airspeed to get close to the top of the low speed awareness bar. There was momentary confusion as to why the aircraft had stopped or slowed its descent; prompting me to disengage the Autopilot and manually fly the aircraft and recapture speed while the First Officer corrected the descent mode by placing us into level change. We had engine anti ice selected on for the ceilings; and turned it off after descending clear of the clouds. We descended to the assigned altitude of 3000 feet and my application of thrust was again delayed or too slow; causing the air speed to again get slow which required excess thrust to be applied. The airspeed was fluctuating significantly with the wind gusts throughout the entirety of the approach; and our approach speed was appropriate for VRef-Ice. The aircraft was fully configured for landing and all checklists completed. We were cleared to land Runway XXL and made a single engine landing; touching down just barely passed the fixed distance markers. I deployed reverse thrust on the right engine and was able to adequately control the aircraft about the centerline of the runway. Due to the nature of the situation; I elected to exit the runway in case any pooled oil began to drip to the ground. I stopped the aircraft on Taxiway 1 to allow ARFF equipment to inspect the left engine. The First Officer deployed the flaps to 40° and I stowed the speedbrakes. The First Officer communicated with ground and ARFF while I made a PA to speak with the passengers to keep them calm and to remain in their seats with seatbelts fastened until we arrived at the gate. We quickly received notification from ARFF that the aircraft engine was free of any fire or exterior damage; so we contacted Ground for taxi instructions to our gate. We taxied uneventfully to the gate where we conducted our shutdown checklist. Immediately following the shutdown checklist; I contacted Dispatch and then was patched through to Maintenance Control. The Maintenance Controller asked for any oil psi indication of 12 or less; as well as the amount of time spent windmilling prior to touchdown. I made sure to include; to the best of my knowledge; all of the requested information from Maintenance Control in my logbook entry. I contacted one of my ZZZ4 chief pilots and then made sure that my flight attendants were OK. During the deplaning process the jet bridge auto-leveler malfunctioned; causing the jet bridge to raise up impacting the forward entry door and lifting the aircraft upward by the door; the weight of the aircraft resting entirely on the door attachment hinge. We stopped the deplaning process while the jet bridge height was adjusted. I added the forward entry door being impacted and used as a lever by the jet bridge into the logbook. Given the nature of the event and after consulting with my First Officer; I elected to have us both removed with pay from the remainder of our scheduled flying; knowing that the reflection upon this event was likely to diminish the likelihood of any possible meaningful sleep.ADDITIONALLY; The aircraft oil had been serviced in ZZZ5 prior to our gate departure. On such a short flight; given our procedure to hide the engine displays after engine start; I typically will not open the engine indications again; per our policy to keep them hidden; until we near our top of descent. On longer flights I typically will look at them momentarily then hide them again once every 60-90 minutes. The auto population of the display got our immediate attention but oil qty was already 0. This occurred just moments prior to my typical oil qty check prior to descent. There is no way to know if in this situation whether or not the loss of oil was sudden or gradual as the engine indications were hidden. The sudden automatic population of the engine indications was effective however at getting our immediate attention once the situation became critical. Cause: Complete loss of oil on the left engine. Allow pilots the leeway to keep the engine instruments displayed after takeoff to monitor more readily the oil consumption of the aircraft. Making this change will allow better decision making; create less startle effect; and perhaps yield a better; and more importantly; a safer outcome for flight crews who lack for total experience. If this was not a sudden leak I likely would have noticed earlier; the downward trend of the oil quantity and been able to better plan or better prepare for a more suitable location away from the gusty surface winds or at minimum been able to reduce or minimize the startle effect of the sudden loss of oil which we experienced or possibly had. While the principle behind the alert concept of the auto population of the engine instruments is well intended; the negative consequences of this policy may cost the company much more significantly in the end; possibly in lives. In short; let us fly and use the tools and instruments available to us on the flight deck as designed by the manufacturer and stop forcing us to hide critical data from view.