This instructable will show you how to strip and season cast iron without using a large amount of lye. Additionally, the seasoning is slick and takes a [relatively] short time to apply.
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Step 1: Strip Old Seasoning
In this step, the old seasoning is removed:
- Wrap the old cast iron with 1-2 layers of paper napkins
- Add 1-2 tsp. of lye to 1/4 to 1/2 cup of water, do this slowly, stir often, and wear gloves and goggles for safety.
- Moisten the napkin with the lye water. Let excess collect somewhere for reuse.
- Periodically reapply the excess to the napkin.
The napkin should turn dark brown, which is the old seasoning. After about a day, the napkins should be removed and the cast iron should be scrubbed by whatever means necessary. If there are still patches of seasoning, the process should be repeated. It can take up 3+ repetitions to strip off really thick seasoning, but it is still easier than scrubbing it off.
Note: I tried using a weaker base (Sodium Carbonate), but found that it barely stripped anything off the cast iron.
Step 2: Neutralize Lye and Rust
In this step, neutralize any leftover lye and remove some rust:
- Wash the pan with water
- Scrub the pan with citric acid or lemon juice
- Wash the pan with water (again)
- Dry the pan with a towel
- Heat the pan on a burner until it dries
Step 3: Seasoning and Post-Seasoning
In this step, season the pan. Here's my "quick" process:
- Heat the oven to 500°F
- Apply a thin layer of oil to all surfaces of the pan
- Stick the pan in the oven face-up
- Let it bake for 30 to 40 minutes
- Remove from oven and let cool for 20 to 25 minutes
- Repeat [2-5] for a total of 3-5 coats, alternate between face-up and face-down
Once this is done, the pan should look "brown" because the oil isn't completely polymerized. To completely polymerize it, the temperature needs to be heated even hotter on the burner. To complete the post seasoning, do the following:
- Put the pan on the burner on "HI"
- Apply a think layer of oil to the inside of the pan while hot / burning
- When the oil smokes, repeat  another 2-5 times (this takes < 20 seconds per application)
- Reduce from "HI" to medium in steps and repeat 
- Reduce from medium to low in steps and repeat 
- Return to "HI" and keep there until smoking stops
When this is complete, you have a slick seasoned surface.