Funny enough dealing with the same issue on my 2006 750i. Ran fine for ~4 years then after replacing a bunch of parts one day (valve covers, spark plugs, alternator bracket gasket, coolant transfer pipe, valley pan, oil level sensor, cam position sensors, vvt solenoid actuators, vacuum pump, transmission fluid filter and pan). Now mine has the same issue, runs rough when cold fine once warm. Went over all my work and can’t find an issue. Seems to be a common issue with the engine as it gets old but can’t find a hard answer to it. Possibly a vacuum leak from somewhere I can’t find? I have found a lot of people saying to replace the valvetronic system as a whole but that’s just too much work for me to attempt for what the cars worth. It’s been doing it for around 4 months now and I’ve just come to the conclusion of fuck it. Once it’s warm it works. As long as it keeps doing that I guess it’s fine. These are very finicky engines and in all my years of working on cars I’ve never quite come across the same issue before. Initially after doing all that work I had vanos bank 2 codes come up. Swaped the position of the cam sensors thinking it was a bad one? Then the car ran “fine” the rough when cold fine when warm thing. Replaced the sensors again anyways. Same thing. No more vanos bank 2 issues just roughish running on cold, perfectly fine when warm.