If the countertop has a large burned or damaged area, it is probably in an inconvenient position. That’s why it got damaged.
If this is the case, you might consider routing out an area of the countertop and installing ceramic tile in the damaged area. This will not only remove the damage, but will give you an attractive place to safely set hot things in the future.
The trick to successfully routing in this situation is to make sure you always leave enough of the original surface to support the router. One way to do this is to route in a spiral pattern and gradually widen the spirals until the remaining material can be easily chipped away with a hammer and chisel.