Which side did you break?
When replacing my passenger-side mirror cap I broke my mirror, it looks like there is a "groove" in the back of that mirror where the material is thinner, thus letting it bend easier and shattering the glass.
I posted in this thread:
https://f87.bimmerpost.com/forums/sh....php?t=1475656 stating I found a replacement glass for the passenger-side for ~$100 (I forgot where, but I can try to find it if you're interested). The M2 mirrors are the exact same parts as many other F-series. The next post after me said they found one for ~$15, so you can definitely find them for cheap!
EDIT:
Also note the the passenger side is not auto-dim (only heated), which makes it a bit cheaper than the driver side mirror.