Hint for 'ya: That is a "counterbore" when it has a flat bottom, and a "countersink" when it has an angle. (Sorry, I'm an engineer, can't help it!)
Best way I've found to do them, if you do not have a mill to use an endmill, is a step drill. Those can be had either from some knifemaking shops, or from a supply house like McMaster.
EDIT: McMaster's supply of them can be found HERE.