I was drilling the last hole (to insert brass rod as hinges) in my
project - cleaning them out after varnishing actually - and the 1/16"
drill bit broke just below the surface.

Anyone have any ideas on how to fix this mess? The jewelry box top is
oak that has been veneered over on the outside and trimmed with ebony.
It is 1/2" thick and the hole is in the side, near the back. I am
highly motivated to repair this rather than try to make a new top.

Suggestions please.

Woodchip