You wipe your carbon steel cookware, and you find that the paper towel is black. What do you do?
First, let's talk about that black stuff. That black stuff can be caused by burnt bits of food that were stuck on to the steel or oil that had not fully polymerized with the steel. If you are using proper cooking techniques like deglazing the pan, controlling the heat, and washing your cookware properly, then this won't be a huge problem for you. It usually tends to be a problem when you are cooking multiple dishes back to back though, so I usually do deep clean once a week as maintenance.
Step 1: Make a Salt + Oil Scrubbing Paste
This paste is abrasive enough to remove burnt on food, but not abrasive enough to damage the seasoning.
Step 2: Scrub with Paper Towel
Use a paper towel to scrub the steel. Feel free to apply as much pressure as you can. The salt will NOT damage seasoning. As you scrub more and more, you will see that the salt turn brown as it picks up the unwanted gunk.
Step 3: Wash and Rinse
Rinse off the salt, wash with soap, and rinse the soap off.
Soap does NOT strip seasoning.
Step 4: Dry Quickly
Dry your cookware with a paper towel or on the stove.
Do not let it air-dry / drip-dry. If you do, it will rust before it dries completely. It is important to dry it quickly.
Step 5: Wipe With Oil
Wipe a thin layer of oil on your cookware to protect it from humidity/moisture. Now your paper towel should wipe clean.
Do this once a week and your cookware will last you a lifetime!