Sharp isn't really what you're looking for, HARD (and sharp) is what you need. Try using a very small, pointed grinding stone with a dremmel, foredom, or small drill (a red or white stone rated for glass work or hardened metal) to start the hole.
First, a few important points. You need to have the hole as accurately centered as possible, so grind (or file if possible) a flat on the exposed bolt surface and then use a center punch to mark the drilling spot. Use a left handed drill bit with a reversible drill. Using a standard direction drill can tighten the bolt even further. Use as small a drill as practical to start and enlarge the hole as necessary with successively larger bits. And lastly a slow speed high toque drill is best, A fast drill in hard metal will overheat a bit quickly.
Once you get a hole started with a stone, switch to a hardened metal rated drill bit (perhaps even a diamond tipped or encrusted bit may help). Use a machinists lubricant with the drill bits and pause often to cool the bit (maybe even have a cold cup of water t dip the bit in). If the bit discolors (turns straw to blue) it's been overheated and will quickly dull.
Be VERY careful not to break the bit or extractor off in the hole, then you really have problems.
Don't forget to protect the opening into your motor at the lower cover from grit, debris and metal shavings. When you get a deep enough hole, tap in a slightly over sized easy-out. Then, with a standard tap handle attached try to turn it out by hand. If it feels like the extractor is going to snap, stop! The hole may need to be enlarged for a bigger extractor (hence the importance of starting out as centered as possible). I don't recommend using it with a reversed drill.

You can also try a very small diameter, very thin carbide disc in a dremmel or drill, to cut a slot in the end of the bolt to turn it out with a screw driver. This will probably cut a corresponding slot on the head as well. If done carefully, with a small enough radius of a disc, and judiciously positioned so the marring to the head is minimal and oriented to pose the least potential detriment, the marks on the surrounding aluminum mating surface shouldn't cause and problems. This would be a last resort proposition, but I have done it before in other circumstances. Also, this would really only be effective if you expect that the problem with broken stud is mainly just getting a firm grip on it and that from there it should turn out somewhat easily (as opposed to being lodged very tightly, cross threaded or rusted in place).

If all that doesn't work, using a wire welder, the method is to weld a washer (with a smaller hole than the diameter of the stud) to the end of the bolt. If the bolt is slightly below the metal surface, the washer should be peened in the center to make contact and then welded to it. Next, weld a nut that is smaller than the diameter of the washer to the washer. The bolt can usually be turned out with a wrench. The heat from welding also aids in the process by breaking bonds between the stud and the threads it's stuck in.

Good luck.