Any solution to getting burn marks out of your bathroom vanity top?

I would mix up some matching 2-part epoxy and fill them in. or do the whole top with a kit like Rustoleum, Gianna or Transformations.... I like the faux marble myself.

Burns are permanent scars. All you can really do is refinish or replace the countertop. I'd suggest you put a placemat or other item in the bath to put the curling iron on so you don't cause more damage.

Backing soda and toothpaste worked for me.

Bobbi gave my answer. Try using a thick paste of baking soda and water, apply and let sit, followed by a light scrub in a circular motion with a soft sponge before rinsing very well.

To stop burning the counter top I put the hot iron in the sink so it can't burn anything.