WIth any luck you won't even need to cut that deep. A 1/16 to 3/32 should be enough unless the screw was binding in the threading. If so you may need to recut the slot with two blades in a hacksaw frame or widen it with the cutoff wheel of a Dremel to allow a thicker blade screwdriver.

It all depends on what was happening when the head snapped off. Did it thread in nicely and then you were just torqueing the head into contact with the brake? Or was it fighting you all the way down the threading? If the first option then you MAY even be able to pick it out using a sharp scribe to nudge it in the hole. With the head busted off there's really no load in the threads and the busted bit should turn easily. If the threads were trying to self cut their way the last little bit than that's a different story. In that case I'd say you need AT LEAST to drill and EZ out the stub. Even that may not be enough if you were putting your all into the project and the head snapped off.

But the fact that you snapped off right at the top of the boss suggests that you were just doing the last torqueing of the bolt. In which case try to just work it out with a scriber before you do anything else. Once you work it out a few turns then you can grab it with some pliers.