B757 Captain reported an engine compressor stall occurred just after takeoff causing the aircraft to yaw. Flight crew set engine thrust to idle; returned to departure airport; and landed safely.

Narrative

ZZZ ZZZZ pilot monitoring (PM) left seat; pilot flying (PF) Right seat. Wx 140/17G23kts 1200BKN 5BR. We elected to use the new wind procedure and discussed it in our threat brief in the briefing area before walking to the jet. Our acft had a distractor; a previous writeup from ZZZ1 which was addressed was about door 1L. The door light would illuminate on the EICAS. We did see it twice only briefly on the taxi out; in each case as quick as it was up on the EICAS it went away. We added to the threat brief that if we saw the light on takeoff roll we would not reject for it. If it stayed on airborne we would then obviously have to address it. We used the software's optimized flap solution and delayed rotation to VR max which was VR+20. Rotation was on the slower side and winds were gusting but down the runway for the most part. Acft weight was 197;000 and runway takeoff data was for 199;000. We discussed the threat of being light and the max thrust for takeoff; which resulted in a slower rotation. Pos Rate gear up came quick and 800 ft was just as quick. We were at V2+25-30 so fast. As soon as PF called for VNAV and I executed the command the engine starting popping and wooshing sound. To the simulators benefit it was very close to the sim experience. So we have a V2 cut; the PF due to the yawing at first thought we had a engine seizure; the popping and having previous experience with Compressor stall. After announcing a Compressor stall we disconnected the autothrottles (AT) and retarded the L Eng to idle. As soon as the engine was pulled back the Comp stall ceased and the engine recovered. Talk about the law of primacy; I did grab the card first before accessing my EFB. Right after the retarding the throttle I [requested priority handling] told Tower we were going straight out and to Stby. At the same time the PF called for VS 100 climb airspeed and AT Arm switch off (which is was). With the Eng stabilized we went to follow the checklist; Gear off; flaps being retracted on speed which was happening quick. At climb airspeed; FL CH; airspeed max con and we were already at or close to 4000 ft. Step 7 had us advance the thrust lever slowly and check that EGT and RPM would follow; they did perfectly. We elected to run the Eng at idle and that we could use it for a GA if necessary. So this is where the checklist could be confusing; step 8 was satisfied as normal then go to 13. We elected to say eng runs at a reduced thrust or idle thrust. I would not want a crew to recover compressor stall and think about continuing. I could see that being slightly confusing. We completed the checklist and the hyperlinks were amazing; hitting the Non Normal config with a landing distance came so fast I thought I might of missed something. I actually referenced it again to make sure I had looked up the correct data; I came up with the same results. We were taking vectors at 4000 ft for the ILS XX. When we input the divert to ZZZ an ACARS prompt appeared to notify Dispatch. I sent a quick dispatch msg with a reply do you need equipment……a distractor that we should streamline. I would like to see that added to the initial prompt we received which was handy and efficient. We briefed the Flight Attendant (FA) via the PA and worked on FMC cleanup. The PF continued and on downwind we were ready for base leg to final; one thing I don't recall is did we request landing data; we might of missed that step. Flaps 20 and GS intercept the PM left the Autopilot on till we broke out. Gusty winds were from 120-140 deg was noticeably present. touchdown and rollout were normal maybe slightly long with late thrust reduction and F20. A missed opportunity for the threat fwd brief as a known result of F20. One critique I had for the PF was thrust reverse were stowed at 80kts; The result was brakes at 3s the 4s. Fire trucks were present and the chief reached out to see if we needed anything and we replied negative. At the appropriate time we shut down the motor and taxied uneventfully to the gate with fire trucks following.