I was reading a service bulletin from some kind of 2010 BMW with similar symptoms involving cold start driving. Turns out it was caused by a fuel pressure problem.
What I’d do is find a shop where they talk, breathe, sleep, and dream BMW with German accents. A shop (BMWs and Porsches parked all over the lot) where what @db4690 said sounds like common sense…
They’d go like, "Well it’s an E93, or F25, whatever, with that N55, WD-40, whatever engine and say, “It no doubt needs the…______________!”
I actually know a guy (a real car genius) who works at such a place. That place would cut to the chase in short order. They’d take it personally.
The corner gas station isn’t going to get this thing running right.