It was supposed to be a nice bit of apple sauce to accompany a fine dinner, but then the door bell rang. Well, -- to cut a long, sad tale short -- the charred apple residue was baked into the saucepan and could not be removed with any of those grill and oven cleaning chemicals we had at hand.
I was time for Inaptly Crafted Man!
Warning: Inaptly Crafted Man has super powers. You may not. If you follow this guide, you may damage your cookware beyond repair. You do so at your own risk! Only apply the method on a plain, untreated hardened steel pan. Otherwise, and especially if it's coated with Teflon and the like, you will destroy your pan.
Start with 120 grit sandpaper and rub in a circular motion with moderate pressure, sanding away the charred residue. Yes, sanding! You'll notice that smaller and thinner spots disappear almost instantly. Continue as long as you hear a scratching noise. At the bottom bend (where the flat bottom curves toward the vertical sides) use a finger to hold the sandpaper and rub sideways along the curve. Stop rubbing if the black spots have disappeared. Replace the sandpaper when it is black. Every so often clean out the black sanding dust by rinsing the pan and then drying it using absorbent tissue paper.
When all of the black areas have disappeared and only shadows remain, switch to 240 grit sandpaper and rub some more. Stop if you've had enough, even if some shadows remain.
Finally, use some steel wool, some water and wet rub it clean for a minute or two. Rinse and dry. You will notice that the pan is hardly scratched at all. Poking and meddling with a fork will scratch it far more. All in all, it took less than 10 minutes to completely clean our pan.
Tip: If you've got a soft sanding block (sort of a sponge with sanding material at its sides), use that instead of the sanding paper. It will sand more gently and adjust to the bends more easily.