I was under the car a couple weeks ago doing water pump/tstat/E93 M3 FSB install. I reached my hand up into that area and was able to feel the top of the stud. Reason why I was poking around there to begin with was to figure out how to get this thing fixed if I ever ended up in the same situation you are in now lol

The stud you broke appears to be the hard to reach one :/ The difficult part now is finding the right tools to get that stud out of there. Once that is complete, you'll have to put a nut at the top (where the stud head is now) and thread a new bolt in from the bottom (which has to be a pretty exact length to keep from bottoming out).

I had to do the same thing for a stud I broke on an exhaust hanger on my bro's G35. Replaced the stud the same exact way as described above with a much thicker stainless steel nut/bolt combo. Call that "unfinished" if you like, but those replacement pieces are way beefier than the stock pieces they replaced.