If your shop (garage) is equipped with a drill press and a decent vise mounted to the press soak it with PB Blaster (or equal), preferably from the back side if the threads are exposed. Then you can center drill the bolt with a small (1/8") drill bit and then use a left hand rotation drill bit, size = whatever you would use for a screw extractor of the appropriate size, and hope that the left hand drill torque backs the broken bolt out. Failing that-If you're very careful and can find the exact center you could drill it out with the appropriate size tap drill (see chart from Bolt Depot below), and then re-tap the threads in the bracket. I'd guess 10mm but I can't know the thread pitch from a photo. Or, a machine shop can probably do the work for you.
How easy it is to fix depends in if you (or the previous mechanic) broke it because you (they) were turning the wrong way or it's really seized up. If it's "just" snapped off it'll probably back right out with vize grips clamped onto the remaining threads or, even better, if you can put a pair of nuts on the threads and then tighten them against each other, then use the inside nut to back the broken piece out.