The best seasoning method I've found for cast iron and carbon steel is the method advised by Matfer-Bourgeat, which is the brand of my favorite carbon steel pan

The best seasoning method I've found for cast iron and carbon steel is the method advised by Matfer-Bourgeat, which is the brand of my favorite carbon steel pan. Clean the pan well, to get rid of the shipping wax if it's a new pan, or scrub it well with salt as an abrasive if it has substandard seasoning already. Then saute the peels of two potatoes in a a generous (at least ½ cup each) amount of salt and oil, while moving the mixture around and using the peels to really rub the oil and salt on the metal, for around 15 minutes until completely crisp and dark. Clean out the pan and repeat the sauteeing steps, clean out the pan again with just hot water and dry it well. No other method has come even close, and it just gets better with more use. My fried eggs just slip and slide around like a hockey puck. If gunk does get burned on, scrub it out with salt and a bit of oil, there's no need to soak or use soap.