A320 Captain reported compressor stalls; engine rollback; and failure of the number one engine while climbing through 4;000 ft. just after departure. The flight crew requested vectors back to the field and accomplished a safe landing.

Narrative

Aircraft X departed the gate on time. We started both engines and taxied to Runway XXR. All check list and engine warmup time's completed. Takeoff roll was normal. After the gear was retracted we notice number two engine oil level was low and started blinking. Shortly after we noticed the white advisory message advising us of the oil. We discussed contacting maintenance once we passed 10;000 ft. And see what they had to say. Climbing out of 4;000 ft. We received violent bangs followed by massive yawing of the aircraft indicative of an engine failure. I immediately leveled the aircraft to get more airflow into the engine. At this point the number one engine had at least 3-5 massive compressor stalls followed by a rollback. My first officer (FO); who did an amazing job; advised ATC and started the ECAM procedures. We had numerous ECAM messages going off and of course flight attendants calling us nonstop due to the flames coming out of number one engine; rightfully so. I immediately started the APU and turned back towards ZZZ. The number two engine was still low on oil so my FO and I discussed the contingency for that situation as well. Once we leveled off; I started a slow decent with reduced power on number one. The compressor stalls stopped but the engine was running hot. Once we had every checklist completed and all the proper company stations called. We decided to make an overweight landing. On final we saw all the Crash Fire Rescue (CFR) was waiting for us. After completing all normal checklists; Fight Attendant briefing; passenger announcements and abnormal checklists; we felt it was time to land. We had plenty of fuel and a lot of time to make sure things were done correctly. Our aircraft weight was around 149;900 pounds when we touched down. We stopped the aircraft in the runway and called flight attended stations. CFR looked us over and noticed our brakes were pretty hot; but did not notice any engine damage or fire on the affected side. CFR told us to shut down both engines on the runway. After inspection I called over the PA to remain seated. We started number two and taxied to the gate with CFR in tow. No further actions were taken.