This is the PCV Heater needing a fused line. But I suspect that the PCV heater has failed and caused issues in the PCV hose, etc.
Does BMW recall replace all parts or just put a fuse in there and call it a day? As I read the SIB, it does state that it can effect the whole PCV system if left long enough and this is a 2010 model.
Never done a recall before.
https://bmwrepairguide.com/sib/110122.pdf