My 04 M54-powered E53 had a leaky injector. Apparently there was a bad batch of Bosch injectors from that era. The symptom was hard restart only when warm. Overnight restart was always normal. I guess the extra fuel had time to evaporate enough overnight or the cold engine's natural desire for richer mixture upon startup made it a non-issue. I replaced all the injectors since they were all vulnerable. Looking at the codes, I was able to determine one was newer, so had been replaced at some point. I kept that one for a spare.Perform leak-down test of fuel pressure; however, if the injector was weeping and bleeding down, you'd also see extra cranking on a cold start.