I agree that an "easy out" is the method to try. If the stud is broken off crooked, use a Dremel tool to flatten or cup the end. That way it will be easier to drill in the center.
If you drill too small of a hole, you would use too small of an easy-out and it might break off. This is bad as you cannot drill out an easy-out. They are too hard.
It is also bad to drill too big of a hole because you weaken the remaining wall of the stud. When you put the easy-out into the stud, the stud expands and will lock in the hole. This also happens if the hole is too close to one side of the stud.
Be patient and gentle, drills and easy-outs like to break.
