B737 Captain reported an Oil Filter Bypass Light caution message appeared while climbing that required an engine shutdown as part of the checklists. The flight crew then performed an air turnback.

Narrative

Climbing through about 15;000 ft. via the ZZZZZ RNAV departure from Runway XXR in ZZZ to FL190; we noticed an OIL FILTER BYPASS caution on the engine instruments. I was the pilot flying; so I told Person A that I had the radios and asked them to run the associated Non-normal Checklist. I was not familiar with this malfunction; but it became immediately clear that there was a possibility that we may have to shut down the engine. I asked Person A to hold on for a second and I transmitted to ATC that we wanted to level off at FL190 in order to work a possible engine problem and that I would get back to them with more information shortly; which was approved as requested. Realizing the possible severity of the situation and the possibility of some very challenging checklists ahead; I decided to swap roles and have Person A fly and run the comms; while I ran the associated checklists for the problem. I started the checklist; which called for turning off the autothrottle and retarding the engine until either the message goes out or it is at idle. I coordinated this with Person A so that they could smoothly apply the needed rudder to compensate for the loss of thrust; which went very smoothly all the way to idle with the message still illuminated. I then knew we were going to shut down the engine; so I took the radios back and with ATC; told them we were returning to ZZZ and needed a turn back toward the airport; and would like to enter a holding pattern in order to run the checklists; and that I would get back to them shortly with the rest of their required information. I then sent a CALL ME message to Dispatch and; while I awaited their reply; I called the Purser and asked them to get out their device because I needed to give them the briefing. They got out the device and I told them that we had to shut down an engine; we are not planning an evacuation; there are no special instructions; we would be returning to ZZZ and landing in about 15 minutes; and that I would make an announcement to the passengers soon.I then called Dispatch on the frequency I was sent; but the transmission was broken and unreadable; so I sent a DIVERT message with a quick note about shutting down an engine and returning to ZZZ. I then went to the Engine Failure or Shutdown Checklist and secured the engine accordingly; turned on the APU for power; and called ATC back with fuel and souls onboard and asked them for a lower altitude. They gave us 12;000 ft.; which caused us to have to use engine anti-ice during the descent; which I selected on for the operational engine. During this time they were vectoring us in an extended holding type pattern. I decided this was a good time to brief the passengers. In a calm voice; I told them that we had to shut down one of our engines; we would be returning to ZZZ; please follow all instructions from the flight attendants; and that I would talk to them on the ground shortly.I then continued to the One Engine Inoperative Landing Checklist down to the items including the Non-normal Configuration Landing Distance table for our aircraft. We were well below max landing weight for the 900ER. At this point; I checked in with Person A to make sure they were ok and on board with everything that we had done up to that point; which they were. I decided to quickly type a more detailed message to Dispatch stating that we had in fact shut down the Left Engine and would be landing in ZZZ soon; to which they replied that everyone had been advised and that we should return to Gate XXX.I then got landing data for [Runway] XYR; loaded and briefed the ILS including the complex procedure for that runway; adjusted the target speed on the FMS approach page; and since we were in heading mode on vectors; I extended the runway centerline off of ZZZZZ1 with a 284 inbound course. I asked Person A if they wanted to also brief the approach because they were going to be flying it; but they were satisfied with everything I had set up for the approach. I then asked for lower so that we could run the Deferred Items Checklist. When we got below 10;000 ft.; I configured the bleed panel; reviewed the flaps 1 go-around with the procedure; and told ATC we were ready for the approach. We were given a vector to intercept the XYR localizer; and since were over 25 miles from the airport; I told Person A that we would need to use LNAV until we were closer in for a better localizer signal. As we rolled wings level; I went to select LNAV but realized the FMS had re-sequenced and the final course was off of the FAF and the magenta line was not far enough out for us to intercept. As I was correcting this problem; we got a TA for an aircraft below us. My immediate concern was that we may have overshot the final approach course; so I told Person A to initiate a right turn and spun the heading bug about 15 degrees right. It turned out that we had not overshot the final and the traffic was just someone climbing out below us and leveling 1;000 ft. below our altitude. I finished extending the centerline off of ZZZZZ1 and rejoined the final. At around 15 miles out we selected approach mode and started configuring for landing. Reaching flaps 15; I ran the Landing Checklist and we proceeded to land uneventfully and taxied to the gate. I thanked the passengers for their understanding and cooperation; then called Dispatch and the Chief Pilot.