TL:DW skip to 7:00
This is my 200th vidja! Incredible how time flies, still having fun in the shop, still making lots of mistakes so you don't have to and still inspiring Trolls to lob spitballs from the knowitalldonothing peanut gallery.
The matter at hand:
I bust a crappy tap and show how to get it out in the home workshop.
There are many moreorless effective ways to remove a broken tap. This is the toughest situation, a broken tap in a blind hole. In a thru hole, you can go for the hammer and chisel brute force method.
Sometimes despite our best efforts to the contrary, things don't go according to plan, so we try something else. Surprisingly, that something else works better than the original plan.

Feeling the weight of all those two dollar coins in your pocket? Throw 'em into the hat and we'll make something out of 'em!
  / ave