Sounds like I have the same issue. Started happening sometime after having the 1200 mile break-in service done. Could it be due to going from a thicker oil that is used when the car is first delivered to the thinner one that is used for the service? Curious if the thicker oil keeps things lubed better when not running because maybe it sticks to the components more. I only drive the car a couple days per week, so I tried driving it every day for 4-5 days to see if that helped, but no improvement. It only has 1800 miles and it's 18 month old. The issue only happens during cold starts and also only happens when in the 750-850 RPM range, then goes away when it fully drops to 600-650 idle. However, I can get the noise to come back if I am able to hold RPM's around 750-850. Does this sound like the same issue as others have had with the incorrect tightening of the cams or something else?
I've also noticed a fluttering sound coming from the engine somewhere between 1250-1750 RPM and around 2500 RPM. It doesn't come across in a video, but I can definitely hear it in the cabin when it's fairly quiet. It also started happening after the break-in service. Searching around the internet and the closest thing to the noise I could find is this.
https://f80.bimmerpost.com/forums/showthread.php?t=1612812
Anyone else have the "fluttering" noise?