I have heard of this problem with Gen2 MINIs (the turbo models), and it seems #4 cylinder is most affected. BMW of course blames it on gas quality, and if you defeat that one, then they claim it's because you don't drive aggressively (which might have some validity actually), if one putters around town all the day long and never gets the tachometer above 4,000.
Sometimes carbon is due to a misfire, so we can't rule that out---might be good to check and see if there are any misfire codes stored in the car's computer.
You might ask your mechanic about running a one step higher heat range spark plug IF you are generally a very conservative driver.
Also, using an additive like made by Swepco 503, or Redline SL1, or BG44K would be helpful.