Magic Eraser
Always trying to keep it clean and help the people.
Enameled cast iron, which does better than regular, uncoated black CI for some things, is easier to keep clean and fresh-looking. Porcelain, basically a melted glass, doesn't like a rough metal scrubbing but loves to soak.
I've been using the Magic Eraser (Mr Clean®) to get rid of the carbon buildup on the porcelain bottom and inside. More about that product later, but digging it for now.
Hack for getting rid of the staining - overnight soak in a few tablespoons of regular, chlorine bleach and water.
This is 18 yo LeCreuset; not sure what results would be with no-name knockoffs, but pretty sure that the Lodge and Staub brands would perform well.
The carbon that didn't come off has been there 18 years...I've learned that as a kitchen boss, you have to pick your battles.