I usually drill out the hole and tap it to the next larger size same for the broken bolt Going up 2 sizes is a little easier if there room for that. If the new larger bolts don't work/fit then I make a stepped bolt/stud with big threads on one end and small thread on the other. Accurate center punching/drilling is important. Left handed bits can be very handy, sometimes they will back out the the broken unit. Kroil is my favorite penetrating oil, used over several days treatment with some heat, and percussion therapy. Welding nuts/washers to the broken unit and try to wiggle it out with alternating tighten/loosening.