Suggestions on removing these broken bolts?
 

These are the two out of three 10mm bolts in an aluminum transmission case for a transmission mount. It's out of the car so access is no problem. I tried to remove the bolts with an impact wrench but the heads snaped off so they are in so tight or rusted that a simple vise-grip probably won't cut it.
http://www.fototime.com/C692BFB3F566691/standard.jpg

I wonder if a craftsman easy out would work in your case. Might work. If you can weld you can always weld the head back on and add strength to it. Heat and PB blaster will be your friend. Just not together flames and pb dont mix.

You can slip a nut over the bolt shaft and weld it...then you put a socket on the nut...

I would do what Arthur suggested AND spray the whole mess with some sort of penetrating spray (after the weld has cooled sufficiently to be NOT flamable).

Treat the area a few times over the course of a day or two with the penetrating fluid and then try to get the bolt out.

If the case is aluminum, you'll be able to get the bolts out with no effort if you use some heat.

If you have a torch, then heat the bolt until it's nearly red hot. Then use a bit of penetrating oil such as Kroil on the threads. Apply the Kroil again in a few hours and allow it to work for about 24 hours.

The studs should easily be removed with vice grips.

Just be careful to keep the torch away from the aluminum.

One of them came out easy with ViseGrips after a few cycles of the propane torch and PB Blaster. The other one took some more effort. After the above attempts failed I screwed on a nut, half it’s thickness down on the bolt so there would be a reservoir to weld into. Then I welded on a nut and while it was red hot I used a can of Freeze Mist to chill and contract the bolt. Then an impact wrench got it off the first time.

Beeswax
 

An older tech I know uses a Beeswax candle (NOT Parafin wax) and heats the metal, applies the candle and he says the beeswax is drawn into the threads and loosens the bond.

Never seen him break a bolt either!