It's impossible to say what the best method for removing a jammed-in threaded part is, without a close-up photo. However here are 3 ways an engineer would do it (and there are many more):
1. Place the Provari in a vice, in a vertical attitude, with the top of the Provari level with the top of the vice. The vice must have soft jaws, or you can use a sheet of leather or similar wrapped around the Provari.
Take a Dremel with a disc cutter and very carefully cut a slot into the top of the snapped-off 'bolt'. Use a screwdriver to turn the bolt and extract it.
2. Or, take a small drift with a chisel edge (a drift is a metal rod, made from steel, brass or ali depending on the intended use), and a light hammer (4 or 8 oz for this job), and using the drift as a chisel, lightly strike the edge of the snapped-off machine screw anti-clockwise to extract it (a 'machine screw' is the correct term for a threaded part like a bolt but with the thread all along the shaft; a bolt is not threaded all the way).
3. Or, if the screw is really hard to extract, you can use a stud extractor: a tapered hardened steel 'screw' with a left-hand thread. You drill a central hole very carefully, then screw in the smallest stud extractor you can find. As it is a left-hand thread (you screw it in the 'wrong' way), when it bottoms out, the broken screw starts to come out. A normal screw won't work because it is a right-hand thread and will only tighten up the jammed part, it needs a left-hand threaded tool to extract a jammed bolt or stud.
I don't recommend an impact driver for this job

(a heavy hammer tool that is whacked hard and turns anti-clockwise as it is struck - works really well on tough jobs but will mash up a Provari pretty good)
Actually your best bet is to take it to the nearest garage with a workshop, they can fix this for you. Just tell them it is DELICATE.