You need the old fashioned soap filled steel wool pad, of which the Brillo Pad is the best known.
One problem with using steel wool, it scratches surface and each time used makes harder to clean,
If I forgot to coat with WUL, I'd store in a plastic bag, to avoid getting soot all over gear. When I got home would put in a basin of water and WUL, leave for at least a day. This would usually make soot wipe of when washing.