I left a pan of rice on the heat too long and the bottom went black. I scrubbed at it for twenty minutes with a scouring pad and made almost no difference.
Then I stopped scrubbing and let chemistry do it, and it lifted off in one piece.
The Method for Stainless Steel
Cover the burnt layer with water — about half an inch.
Add two tablespoons of baking soda.
Bring it to a simmer for ten to fifteen minutes.
Take it off the heat, let it cool until you can touch it, then push at the edge of the burnt layer with a wooden spoon.
It should come away in sheets. If it does not, simmer it again for another ten minutes — the answer is more time, not more force.
For anything really bad, add a splash of white vinegar once it has cooled a little. It will foam. Leave it an hour.
Why It Works
Burnt food is protein and sugar that has carbonized and bonded to the metal. Scrubbing tries to break that bond mechanically, and steel is harder than your sponge, so you mostly just polish it.
Simmering water gets underneath the layer and softens the bond. Baking soda is alkaline, which breaks down carbonized protein specifically.
Together they release the whole layer rather than wearing it away a bit at a time.
Non-Stick Pans Are Different
Do not use baking soda, and never use anything abrasive.
Hot water with a drop of dish soap, left to soak for an hour, then a soft sponge. That is all a non-stick pan will tolerate.
If the burn will not come off a non-stick pan, the coating is probably already damaged and the pan is finished anyway.
Cast Iron Is Different Again
Coarse salt and a little oil, scrubbed with a stiff brush or a chainmail scrubber. Then dry it on the heat and re-oil it.
Do not soak cast iron and do not use baking soda on it — the alkali strips the seasoning you have built up.
What Not to Use on Anything
Oven cleaner. It works, but caustic soda pits aluminum and strips any coating. Not worth it on a pan you eat out of.
Steel wool on anything but bare cast iron. It leaves scratches that burn on faster next time, so you are making the problem permanent.
Bleach. It does nothing to carbon.
How to Not Do It Again
Most pans burn because the heat was too high, not because you forgot them. A thin pan on a high flame has a hot ring in the middle and burns there first.
Medium heat and a heavier pan solves most of it.
And keep the baking soda where you can reach it.

