If it's a blind hole and you can put it into a position where a liquid
will stay in the hole. You need a few items.

One a heat gun or torch to heat the aluminum part so it is very warm.
A jar of ALUM (Spice sold in a grocery store, usually used to pickle foods)
Clean water.
Some Play Doh or modeling clay.
Small brush.
Needle nose pliers.

Alum has a neat property that we are going to exploit, it doesn't like
steel.

Set up your part so the hole is up where you can see it. Now make a dam
around it so that it will hold more water. Drop some alum into the hole
and use the brush to get it down around the steel as much as possible.
Now add some more alum and some water, you want it to end up a thin
slurry of water and alum. Now use the heat gun or torch to heat the area
around the broken bolt, Don't get it to hot, you want it to get just hot
enough to be uncomfortable to touch. Use the brush to stir the slurry
while you heat the part. Add some more water as it evaporates. Watch for
the slurry to turn black and ugly as you stir it. That is the extractor
and bolt dissolving into the alum. It will dissolve enough of the
threads to loosen the bolt and allow you to remove it in 20 minutes or so.

Then just wash out the hole and clean up the threads with the proper die.

You can also use diluted nitric acid (1/3 water - 2/3 acid) but it gives
off nasty fumes and is dangerous as well.

I've removed many broken bolts by locating a loose nut over the broken
bold and mig weling inside the onto the bolt shank. Jesse