The hard tool steel of the easy out will just force the soft brass to expand in the hole. I predict the next thread to be "broken off easy out in aluminum housing." Those things are a pain in the dick. I've seen them work exact twice. Ever.
If it's broken off flush, then slot the broken bolt and try to take it out with a screw driver. If it's just too deep to slot without destroying the housing, then try a small punch to drift it out.
What kind of tools do you have access to? If you have access to an end mill then use a carbide drill center to make a center dimple (those things are the tits) and just drill the brass out to 75% the thread depth. A tap should just peel out the old screw threads from the aluminum. A plug tap is better than a taper tap for this mess and It is better at catching the old threads.
Probably less of a headache to just buy a new part.
If it's flush then I would honestly try to notch it and remove with a screwdriver first. Brass is very soft and won't take much to remove. I've done this many times in the past with air/fuel mixture screws. Only issue with trying the easy out first is that if it doesn't work then the notching can't be done. Best of luck..
So, ItsnotLupus, you win the prize for closest to the actual prediction. Except the easy out didnt break. It grabbed real good. So good in fact that it expanded the brass insert and broke the aluminum housing all to hell. Sooo time for a new carb bowl. That brass was absolutely fused to the aluminum. The end mill routine would have worked. (Don't have one of those in the garage.) Anything short of that was bound to end this way. Sure glad I have a parts motor sitting 10 feet away.