I don't know if this will work, but it did back in the day when I was in 7th grade home ec and we had plenty of burned pans:
Add water and simmer, working at the crust with a wooden or nylon spatula. Basically, you're deglazing the pan. Get as much off as you can that way.
For All-Clad, NEVER use an abrasive scrubber or cleaner. Use Barkeeper's Friend cleanser only. Use that for the rest of the residue. As Pan said, it should clean up. Let us know how it comes out! We'd like to see the "after" picture, too.
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