B757 First Officer reported returning to departure airport after experiencing loss of oil in the left engine.

Narrative

The weather was not a problem as we were planning to leave ZZZ. There were normal flows and timing on the ramp and we taxied out to RWY XXR with no problems.We took off and switched to Departure. Captain and I noticed an amber indication on the OIL TEMP on the left engine. We talked about it briefly but were given further ATC instructions to climb to FL200 and switch to another frequency. We noticed the OIL QTY read 0 on the left engine stack but was still white like normal. We reached FL200 and asked to stay at FL200 to run a checklist. We pulled out the QRH and ran 'Engine Oil Temperature (PW)'. We ran through the checklist and retarded the throttle and started a clock. Captain talked about where we should go and I mentioned returning back to [departure airport] since we left there. Captain mentioned we should ask [Company] but at that time we were watching the OIL TEMP and he was continuing to retard the throttle and the Oil Temp continued to rise. The Oil Temp went from amber to red and smoke began filling the cockpit. I immediately donned my mask and watched Captain put his on. During this time; he shut down the engine as I was kind of in shock. After a few moments; the shock wore off and I think at this time asked [for] direct to ZZZ with a descent. We were given direct and a descent to; I think; 5000 ft. ATC became distracting at this point asking for our problem and I think I told them standby. They asked again and I was somewhat terse saying we had smoke in cockpit and shutdown an engine with two souls on board and fuel for at least 4 hours. After that Captain asked me to confirm the engine was shut down and I pulled out the QRC for 'ENGINE FIRE or Engine Severe Damage or Separation' (We did not have fire lights; but I think the smoke led us to do this over engine shutdown in flight (it happened very fast)). I ran through the steps and confirmed what he had done and then pulled the Engine Fire switch (which is way harder to push the button and pull the switch out in the airplane than the sim). He told me to put in the approach and 'nuke' the box. I was somewhat struggling mentally and fumbled my way through it and Captain was having to be quite directive. I asked if he wanted the QRH for 'ENGINE FIRE or Engine Severe Damage or Separation' and began to go through the checklist over interphone. Captain continued to fly and we ran through the checklist (looking back through checklist I read through all the steps; but I don't think I verbalized everything). Halfway through the checklist is when the fog and the startle of the event began to pass for myself and mentally got back into the game. We stayed in that checklist and I talked with ATC and ran through everything. Time finally felt like it was slowing down when we were getting vectors to final. We got on final and ran through the deferred items and Captain made a really nice 20 flap landing with gusty winds. We taxied off and let fire and rescue look over the left engine. They told us they saw nothing so Captain made the call that it would be safe to taxi back to ramp and much quicker than waiting on a tug. We taxied back with no problems and shut down normally. I noticed that the clock that had been running was at either 37 or 39 minutes since we started timing the engine oil temperature. Everyone met us at the jet and we opened the windows and then got out of the plane.The cause of the event was the oil departed the left engine. Oil found on underside of wing and engine blades. Further investigation of the engine would give insight into what went wrong and how it possibly could be prevented.