Machinist here. Drill that bolt the rest of the way out and see what size hole you end up with. If you do a good enough job, you should be able to drill and tap it for a helicoil that would be the equivalent inner thread of what was there previously (just please use metric, it makes you look bad having standard mixed in on a jap car). If the hole ends up a little too big, check the next size up helicoil and see how much bigger you'd have to make the hole in the transmission for the slightly bigger bolt to pass through.

If the hole ends up too big/wallowed out for a close enough helicoil, you're gonna have to go for a stainless steel threaded insert (avoid brass and anything that has cutting teeth on the OD threads, that's for wood). Make sure to use RED loctite and DO NOT bone this one up. Take your time and do it right. Make a guiding block for the tap to go through so that it isn't at an angle and make sure you drill the hole straight to begin with. The next option I can think of is having that area built back up by welding, having that surface machined flat again, and a new hole drilled and tapped.

Pro tip for getting the rest of that bolt out: Get a left handed drill bit and run your drill in reverse. If you're lucky, the bolt will just thread on out once it catches and you'll have good threads and not have to mess around with helicoils or inserts. If it's being like most automotive work, it'll be the same amount of effort as a right handed drill bit to get through that broken bolt. Use carbide or cobalt bits. HSS works in a pinch, but it's slow goin. Keep RPMs low and pressure pretty high.

Good luck! If you have questions let me know. I make airplane, boat, camera and gun and car parts for a living. So I kinda know what I'm doing with threads.