Machinist’s woe: How the hell do I fix THIS?

So I was tapping a stringer on Keyboard 1 and the tap snapped off in the hole.

Below the surface. That’s hardened steel. Drilling it out so I could use a reverse-extractor was fruitless: I blunted, this and finally snapped a cobalt bit, which the hardware store said was the hardest thing they sell.

Now WTF do I do? Anyone have any brilliant solutions? Please forward this to all the metalworkers you know.