I would get a piece of formica and do some experimenting, but I would think that you would need a ceramic tile bit to drill the pilot hole. If the hole is to be 2 inches in diameter, then I would try a hole drill that you use for door knobs. Take it real easy and slow.
The problem is that the formica might not take a drill and start splintering up.
Consider making a rough jagged cut, then use a countertop router bit to smooth it out and round it out.