Thanks, all, for your helpful responses! I've tried all of them, except for the solution with hydrogen peroxide, with moderate success. I trust that I'll be able to get the pot (close to) completely clean in time.

Yep, the boiling water and baking soda trick worked perfectly for me. I even forgot it on the stove and boiled it down to dry and figured I really messed it up now. Nope, put some hot water in there and everything came right off with a PLASTIC scaper. Phew!!!

Hydrogen peroxide. A touch of baking soda. Heat it--it needs heat to make it react with the carbon.

This is especially great for sugar based carbon burned bits.

I burned some orange peel I was candying a couple years ago in a Le Crueset that I didn't think was ever going to come off. The most successful thing I tried was to bring a bunch of water in the Crueset to a boil and add 2 tablespoons of baking soda and 1 tablespoon of vinegar (any kind will do, so go cheap). It will go all foamy on you like a science experiment and then subside. Let boil for about 1-2 minutes and turn off the heat. Let the water completely cool to room temperature and then try again to remove the burned stuff with a wooden implement. This works on all kinds of pots. And don't feel like you have to carefully measure the BS or V, I just pour them in to approximate the right amounts.

Add white vinegar to the pot and bring that almost to a boil. Use a wooden spoon to move the gunk off the bottom.

Failing that, Bon Ami works pretty well.

I would try two things. First, fill the pot with water and set it to boil. That should boil off most of the residue. You may need to change the water a few times. Or pour boiling water from a tea kettle into the pot.

Second, use white vinegar. Allow the pot to soak in white vinegar for a couple of hours, then scrub with a plastic scrubby as to not damage the enamel.

If these two methods do not succeed, buy Barkeeper's Friend or Bon Ami (huge container for less than $1). It's basically diatamecous earth, and it should get rid of that black residue.

I would put baking soda, dish soap, and water, and heat if for awhile on low heat, then try to scrub it. The heat should help soften up the gunk.