Your out of luck on that. Once Formica or any other laminate top gets burned you need to replace it.
You can however paint it. Much like folks do to the kitchen counters. Do a search on top of page for painting kitchen counters and check out all the great jobs that folks have done.
Does anyone else have any suggestions?
Laminate tops such as Formica are made from paper and plastics. Once the plastic surface which is the pattern or the color it is damaged beyond repair. This happens a lot in kitchens when people put hot pots on the counter. The heat causes the laminate to lift and darken. And also quite a lot for the very same reason as you.
If the top is still smooth, it can be painted. If its a solid color you could match it if you like, or there are counter top kits that will make the counter look like granite or marble. Its not really hard to do. Here are two links for some ideas that may help you out.
I'm there with Woodbridge...your pretty much looking at some paint or resurface option.
I have seen a number of "ready made" granite tops at my local home center that are pretty economical compared to custom fabrication options.
One of the greatest assets of real granite is it is resistant to heat.
The link above includes a pre mounted porcelain sink.
Put toothpaste, one that has some "grit" in it on the surface, wait 15 min. then slowly rotate toothbrush on it. It won't take it off but will look much better, than you can add a little paint.