You really have to have a go at trying to get the broken stud out first, drill the sheared off bolt out and use a helical stud extractor and heat to see if you can crack the thread. If the thread is really tight and will not move, then its a drill and tap out job. Try to drill the hole exactly in the center of the stud and keep the drill as vertical as possible. Drill out at tapping size, then re-tap the new hole using a three stage tap kit. You may find that the tap brings out the rest of the old bolt and you get a reasonable tapped hole. If the new tapped hole is not good, due to thread interference from the new and old threads, or because the hole is not drilled accurately, then the hole needs tapping for a helicoil insert. Drill and tap out for a helicoil, usually a helicoil kit has the correct taps and drills with it. If the thread was a crimped in one, then you can get hankbush kits to just simply drill out and re-crimp in a new insert.
Finally if your thread can be accessed from the other side, you can use a simple nut and bolt.
Make sure you can torque up the new bolt to the correct setting before you are happy with the result.
Helicoil kit
Tapping a hole for a helicoil
Helicoil
And fitting one
Sundance