Go buy a non Chinese, quality set of stud extrators ( other wise known as ezi-outs) a set 1/8" drill bits
and a tap & dye set for around $40 made in China, for now.
Get the expensive one's later when you practice on the cheap set and they give ya the ****es.
Use the 1/8th drill bit to drill a hole dead centre of the broken stud, use the ezi-out to remove the stub, incase you miss drilling straight dead centre with the drill, use the M6-1.0 tap from the tap & dye set and clean up the thread.
Use some oil when tapping the thread.
If you mess up and the engine is still new, send it back and ask for another, cos this is nonsense.