Ok I may be about to make your day.
The rotary encoder seems to be part of the $180 face plate not the $2000 infotainment computer.
https://www.turnermotorsport.com/p-1...uine-bmw-part/
That's for a new part. Look on eBay for a used one.
If you get a used working faceplate, send me your old one if I can find the encoder and replace it can sell the fixed one on eBay and may cover much of the cost.
$80 eBay. Hi
Careful on model number. I used realoem for wife's 2012 I didn't catch what year is your car find the exact part using real oem and search eBay.