Honestly this works but only in some circumstances, but seriously if the situation permits try it and you'll be surprised. My grandfather, a farmer and machinist taught me this trick.
If you take common lye, also known as draino, mix up just the slightlest tiniest bit of it, get an eye dropper and drip a couple drips into the hole with the broken easy out in it, or also works for broken off taps, and put a bit of wet with the same fluid bit on kleenex or tissue on it to keep that fluid from drying overnight, by morning or 8ish hours later you'll find that tap or easyout will almost litterally fall out on its own.
Only problem with this trick is that the stituation must allow the liquid to pool in the hole containing the broken tool so most sideways and all upwards facing situations are ruled out.
I know it sounds weird, but seriously it really does work every time, easily too.