Milling machine with a solid carbide end mill will machine the stud out without any problems. You could use a pillar drill but you'll need to use split collets with the end mill as a jacobs chuck will not grip the end mill's shaft correctly.

Either that or, I would personally try the easiest thing first: Weld a washer to the stud then weld a nut on top of the washer, then use the nut to try and undo the remains of the bolt

Famous last words but it should be pretty quick and easy job