First Officer reported #1 Engine flamed out at cruise due to a fuel imbalance. The flight crew descended to restart the engine and returned to the departure airport.

Narrative

I was Pilot Monitoring and the PIC was Pilot flying for this flight. A fuel imbalance existed between the main tanks with the left tank being about 500 pounds lower than the right. The cross feed was turned on to correct the imbalance and we got it to stabilize at about a 600 pound difference. While at a cruise altitude of FL360 we received a master caution light indicating 'LOW ENGINE IDLE'. We noticed that the left N1 was falling and then the autopilot kicked off. Pilot Flying took control of the aircraft and we quickly determined that we had lost engine 1 and we were going to return to ZZZZ. ATC was informed of our desire to return and [requested priority handling]. Number 2 engine gauges were indicating normal and number 1 engine gauges were not indicating anything abnormal aside from the failure; but the all three fuel gauges read '-0' before eventually returning to accurate fuel readings a few minutes later. We descended from 360; ran the 'Engine Failure' and 'Engine In- Flight Start' QRH checklists. We started the APU at FL240 and performed a starter assisted engine restart around FL190. We successfully restarted engine 1 and returned to ZZZZ without further incidence. Currently undetermined. Potential fuel flow issue; maintenance is looking into the event.