I love using my cast iron skillet and carbon steel wok, but on occasion I'll forget to clean them right away and I'm left with a stuck-on gooey mess. Soap will destroy the seasoning of the cookware, so what I do instead is get everything possible out with a steel wok spatula and then use a salt scrub for anything remaining on the surface.
Gardening blog Our 20 Minute Kitchen Garden provides a straightforward salt scrub technique: Add a light layer of salt to cover the bottom of the pan and use bunched-up paper towels to scrub away any food particles stuck to the pan. Salt is a natural abrasive and does well in this task. Discard the soiled salt down your drain or in your rubbish bin and briefly rinse out and immediately dry your cookware.
Instead of drying with a towel I generally put it back on the range until any surface water has evaporated. Cast iron or carbon steel cookware will last nearly forever, but the season is delicate and needs to be protected. If your cookware is properly seasoned you'll find it is naturally nonstick, but any stubborn food particles can be removed easily with a salt scrub.
Cleaning Cast Iron Cookware: Salt Method [Our 20 Minute Kitchen Garden]