When a tap breaks, it is unlikely that it will break flat. Most tend to break in an oblique direction leaving you with an odd shape to work with. If you are able to clamp it with pliers or vice grips, attempt to unscrew the tap.
If this doesn't work there are a few things you can do. File down the remaining section using a grinder/belt sander. Then you can:
Use a pin punch and hammer and try to punch out the broken tap. Then re-tap the hole with the same size. Often there is enough thread to make this work.
Centre punch the tap and drill out the tap. Most taps are made from hardened steel and it is unlikely that you will be able to drill through the centre of the tap. Use a cobalt bit if attempting to do so.
Use a carbide burr with a dremel tool and try to take out the centre.
Invest in a screw/tap extractor (expensive)
Get a new upright!