Having to remove a a broken tap is really not a fun situation to be in.
But with the help of some proper tools and techniques all taps are removable.
Plan A: Walton Tap Extractor
Get a set of Walton Tap Extractors, they have arms that go into the open grooves of the tap.
Sometimes however, the taps are just too far stuck to be removable with the walton tap extractors and they dont work:
Plan B: Shatter the tap after freezing
Taps are made of very high strength steel, and because of their high strength are brittle. Coincidentally the very reason most taps break is because of their brittle nature.
What many people don’t know is that brittleness changes relative to temperature, and in the case of steel and iron, the affects are dramatic.
Carbon is the primary driving factor behind the hardness of steel. As illustrated, all levels of carbon are affected by temperature change.
Using carbon dioxide in the form of a computer duster or other carbon dioxide supply is the easiest method to flash freeze taps. Carbon dioxide when rapidly decompressed creates dry ice, which can hit a temperature of -78.5 degrees Celsius (-109.3 degrees Fahrenheit). At such a low temperature the tap becomes extremely brittle, and the use of a punch normally will lead to the tap shattering into many small pieces which can then easily be removed.