DIY machinist drilling problem
First try to determine if the piece is a solid piece of steel or a casting, sometimes referred to as potmetal. Over heating a casting can turn it to a brittle paperweight The broken extractor bit is likely to hard to drill out. If you have access to the opposite side try to drill a small hole and drive the broken extractor out with a punch. Once the broken bit is removed drill and tap it for a larger screw, install a heli-coil or a nutsert.