Oven seasoning your carbon steel skillet is a bit more time-intensive, though it is also more thorough and less of a smokey mess.
The same principles are present in this process as in smoke seasoning. Essentially we are opening the pores of the steel, introducing a medium-temp oil, and heating that oil beyond its smoke point allowing the oil polymers to bond with the metal.
This method is also the best method for restoring even coloring to the entirety of your pan.
Begin by thoroughly cleaning your skillet; scrub with a light abrasive, remove any carbonized food and try to remove as much oil and shine as possible.
Once clean, place in the oven at about 300 degrees until it is dry and warm.
Remove from the oven and let cool a bit, we want it warm still but not too hot to handle.
Use a medium temp oil, flaxseed, coconut, canola…etc. and coat the entire pan, inside and out. Once it has been liberally oiled wipe the pan down so that the steel is not too greasy but well moisturized.
Turn your oven to its highest heat setting. Once at temp, place your skillet upside down in the oven on the middle shelf. You may want to place some foil on a shelf beneath to prevent oil from dripping and flaring up.
Bake your oiled cookware for about one hour. After an hour, turn the oven off, let your cookware cool in the oven. Once your oven and pan are cool, remove and inspect. Your pan should have a matte sheen and be darker in color than prior to seasoning.
This method may be repeated as many times as you like until the pan is dark and well seasoned.