Broken Exhaust Manifold Stud

Your pic isn't to clear but it looks a to be just below the surface. Also the head appears to be still on the engine. Still in the car? The welding fix is a good one. If you have access to a mig even better. Center a washer over the hole/stud, weld the washer to the broken stud. It may take a couple of tries to get the weld out to reach the washer. Slow and easy. Try to get a good initial bead(penetration) on the stud. When you get to the washer use the thickest one you can find. the hotter you can get it now the better. Lastly weld a nut to the washer. give it a couple of minutes to cool and work it back and forth with a wrench. Most of the time it will work on the first try. If not do it again. The heat of the weld helps loosen the stud and break up the rust and gunk on the stud.

Good luck.