Seized bolts can be a PIA, but the job is definitely achievable.
Start with PB Blaster or equivalent on any exposed threads on the broken bolt, and give it time to penetr*te (didn't know it was a forbidden word here) downward into the threads of the broken bolt. A few applications over a long day should provide the best penetr*ting results that you are going to get from it.
Then CAREFULLY use your centering punch to create a small indent as close to the center of the broken bolt that you can. Don't worry if it is slightly off center.
Then start drilling with your smallest drill bit. Apply light steady pressure to the drill, but not enough to overheat or snap the small drill bit. Be sure to liberally use cutting oil, applying several times during each drill bit progression. You don't have to drill clear through the broken bolt, but estimate the drill depth to be at least up halfway through the nut. Progressively increase the drill bit size in small increments, being patient and consistent. The broken bolt will free up long before you get to a drill bit size that could potentially impact the nut's threads.
Then, use the correct size thread chaser to clean out the nut. Purchase the correct replacement bolt, and put liberal amounts of basic Loctite on the replacement bolt to prevent the threads from seizing up again, in case you need to remove the bolt in the future.
