I've only bought the pan a week ago and used it three times. Hot dogs, eggs, and steak.
When I'm done I clean it with a scrubby sponge and once with a little bit of detergent, then put it on the stove to dry quickly. Then while it's hot I smear maybe a teaspoon of vegetable oil on it with a paper towel "brush".
In between uses it's wet with oil, as you can see in the picture. How much residual oil should there be? I had the impression that it would be dryer.
Also, how much should I scrub? I am not going to leave crust of beef on there, but I also don't think it's supposed to be scrubbed back to new smoothness.
You can scrub a cast iron pretty hard if you're just using soap and a sponge. I'm sure you've heard that you shouldn't use soap with cast iron, but that advice comes from a time when lye was an ingredient in most soaps. Dawn isn't going to strip the seasoning off your pan.
You can scrub the hell out of it too, but you have to be care about abbrassives in the pan. A new dish sponge will scrub burnt stuff from your pan. A new dish sponge plus something coarse like a bit of kosher salt will strip the seasoning. That is useful if you want to entirely strip and redo the seasoning, but for routine cleaning you want to make sure you're scrubbing it, not sanding it.
Oil in the pan between uses: I'm super neutral on this one. I leave mine dry between uses, and I have to touch up the seasoning every three months or so. My parents store theirs with a very thin sheen of oil (pour in a drop of oil, wipe it away with a towel until there are no visible pools or raised lines of oil) and they almost never need to re-season. Imo both are reasonable, I personally prefer the dry storage because occasionally touching up the seasoning feels like less work and less waste than oiling it after every use for storage.
I do the same as you after most uses. Scrub with dawn, rinse, dry. Done.
Thank you for sharing. I'll really need to try some of these various methods.