Have you got it loose yet?
If not time to break out the heavy machinery. File a flat spot on the top of bolt, or broken stud and center punch it. In your case, simply centerpunch the center of the machine screw. Now start drilling. Do you have other bolts out to figure out how long it is?
Center punch, use a centering drill bit and drill down through the bolt. Hold the drill straight, don't flex the bit. Use oil
to lubricate and cool the bit, don't make big fancy spirals start and stop pressure once the chips start to flow so the heat leaves with them.
Once you have a straight hole, enlarge it. Drill out as big as you feel comfortable without getting into the threads in the part. Doing this relieves the bolt. Bolts are under tension, as they thread in the threads try to stretch the bolt out. Relieve most of the metal from its inside, it gets loose. Sometimes it is helpful to grind the head
off to relieve further tension... last resort!
Now, don't go reaching for an easy out. Tap a left hand thread (or right hand if the fastener is left hand) into the hole, go get another fastener, preferably one that goes just shy of bottoming out. "Tighten" the left handed thread and it should back out the leftover threads in the old bolt.
Use as high a grade of bolt that you feel comfortable drilling... More than 5, less than 8...
So if it breaks off, you don't have to drill something super hard. When you snap an easy out, it means ten times the work.