Looking for options on removing a 1/2 inch threaded galvanized pipe broken off with about a third of an inch of it still inside the hole.
Mazura's answer describes the best solutions.
But if there really is only 0.33" inside the pipe and part of the broken pipe remnant is protruding from the intact pipe, you might be able to manage without special tools if you take a slim metal-cutting hacksaw blade and carefully saw a channel all the way through the wall of the pipe fragment, parallel to the direction of the pipe. (Be very careful to avoid cutting into the intact portion of the pipe!)
Then take a rubber mallet and use it to tap the blade of a stout flat-bladed screwdriver against the protruding lip of the broken pipe next to the channel you have cut, so that the cut edge of the pipe you were sawing is pushed a little way into the void. This should loosen the pipe fragment from the thread of the intact pipe, and also create enough room to allow you to grip the broken bit of pipe with some needle-nosed pliers and then work it free.
FYI: A neighbor (in the physical world) wondered by and had the perfect tool. Expanded details: https://ello.co/cwhii/post/W6vBG5nnYlOSFK6ciW0SBw
I had this problem today. 1/2" of 1/2" thread left inside the pipe. Logic said that if the tap was that rotten then the remaining piece in the pipe would be the same or worse. It had snapped off flush so no edge to work on. Where I could see the join I placed the very corner tip of a coal chisel on it and gave a gentle tap. It shattered! Job done The moral being that "It don´t take a sledge hammer to crack a nut"!