B737 Captain reported engine failure during cruise and return to departure airport.

Narrative

As we were about to level off at FL370; engine #1 rolled back indicated by a yaw; a low oil pressure light and disconnection of Command System A. As the PF; I said my aircraft" while assessing what took place. I hand flew and asked the FO to request assistance and ask for lower. I asked for FL250 and FO relayed. We were initially given FL340 and I started a slow decent while hand flying. ATC asked for our intentions and we told them we would like to return to ZZZ via vectors. FO then assessed the QRH via his EFB and asked if I wanted a checklist. We were still trying to asses the problem and decided to run the "Engine Failure or Shutdown" checklist.I told FO "my aircraft and radios" while we ran the checklist in tandem. ATC (ZZZ Center I believe) gave us FL240 and I slowed aircraft to best single engine drift down speed per FMC (about 248-250 kts). ATC SOP's continued with request for SOB's; FOB and exact type of situation although I believe FO had already given them the latter.I trimmed aircraft and engaged Command System B as we continued descent. I then sent an ACARS message to Dispatch while FO continued running the checklist. I should have used ACARS code but had run out of bandwidth at the moment and just sent a "free text" message.We finished the "Engine Failure and Shutdown checklist" and FO continued to the "One Engine Inoperative Landing" checklist and verified landing distance via the performance tables. We talked about the Go Around procedure review and possible issue with fuel balance. It wasn't an issue as we were still feeding from the center tank.At this point; I told the FO to take the aircraft (still descending to FL240) so I could focus on communicating with FA's and passengers. I went to the "Non Routine Landing Considerations" checklist. FA #1 had called because she felt something wasn't quite right and we told her she was correct and that we would get back to them. I now got both front and back galley on the phone and briefed them about a precautionary landing via item X on Precautionary Landing checklist and followed up with a PA via item Y.As we were about to level FL240 I took the aircraft again and FO became the PM. ATC gave us direct ZZZZZ and a descend to 14;000. Then 8;000 PD. Autopilot was acting a little erratic in vertical mode. Even as the aircraft was trimmed and autopilot engaged; it kept going into vertical Control Wheel Steering (CWS) mode. We tried to disconnect AP and FD's and then re engage (always both in VS and FL Change); but same result. I chose therefore to hand fly from about 14;000 and down.We had requested ILSXXL for landing. We briefed it and again looked at the potential single engine MA procedure (had flown in/out ZZZ the last three days) and built it in Route 2.Checked in with ZZZ Tower and was cleared to land RWYXXL. Airport Rescue And Firefighting (ARFF) was on the frequency and standing by. When asked our intentions after landing; we said we would come to a full stop and get inspected by ARFF and then proceed to gate. When asked again while rolling out we decided to clear RWYXXL at XX and come to a full stop while ARRF inspected left engine and brakes for damage and temperature. Landing weight was below MLW at about 144;000 lbs..We were told everything looked normal; so we were cleared to continue taxi to gate XX. Normal single engine taxi followed and shutdown flow and checklist ensued.Cause: Not sure what could have prevented this. At least from a flight crews perspective. But I commend our training and procedures in making it a somewhat routine process getting the aircraft on the ground. I could probably have done a better job being situational aware of location and closet airport as the engine rolled back; but knowing the DP points on flight plan before TO gave me good SA of ZZZ as nearest suitable. Procedures and my FO's knowledge of them; also made the process seem routine. As I was still trouble shooting and flying the AC; he; as PM; recommendedstarting the QRH Engine Failure or Shutdown checklist and went through with exactly the cadence needed for me to keep up while flying and talking to ATC."