I was burning a cone incense and left it on the sink, and this stain won't come off. I tried baking soda, water, vinegar, hydrogen peroxide. I tried letting them sit for multiple interations, and it made no difference.
You can not.
This is not just a surface stain, but it has literally changed the material underneath the burn.
Amy attempted fix will just be an obscene amount of work for what will still be an obvious repair job.