This is something I found by accident looking up something else, it's about the latest petrol engines sounding like diesels on idle, may have some bearing on what you are hearing:
What BMW don't want you to know (or notice), petrol engines with all the finesse and refinement of an agricultural diesel engine.
Apart from the faults experienced with this 3 series (330i SE Coupe), there is another issue which BMW do not want people to notice and it exists with all their petrol engines since the N53. The lean-burn engine, first introduced in 2007, includes a fuel-injection system known as High Precision Injection. Unfortunately their new petrol engines sound a lot like diesel engines and under load you can actually hear diesel clatter and other similar noises from what should be a very quiet and refined petrol engine. Also, the BMW six cylinder engine - once famed for its smooth and almost undetectable operation while running at tickover or idle has lost all of its characteristic heritage and is now noisy and unrefined. It is a major step backwards all in the name of lower emissions.
This they describe as JOY. Any BMW with this recent injection system will sound more like a taxi or a delivery van. Not good for a prestige motor car which anyone might expect to sound like - a prestige motor car!
If you own a BMW with the earlier engine N52 engine, hang on to it.