An hour before cooking, cut the eggplant into 1/2 inch cubes, place in a colander over a bowl and sprinkle with a tablespoon of salt. Mix well to coat. This will help the eggplant release its bitter juices.
Right after you prepare the eggplant, sprinkle some salt on the fat side of the chicken thighs, both on top of the fat and on the other side of the fat. This will help expel moisture and allow the skin to crisp better. This should be done an hour before cooking as well. Place them in the fridge, preferably on a wire rack over a plate.
Slice a medium size onion into thin slices, cut up a red pepper into 1/2 inch pieces, and peel 4 Roma tomatoes, then remove their cores and seeds and chop them into 1/4 inch pieces.
When you're getting ready to cook, preheat your oven to 425 degrees Fahrenheit. Pull your chicken thighs out of the fridge and dry them off thoroughly with paper towels. Don't forget to dry them off underneath the skin as well. Season both sides with pepper, but no salt. Arrange them in a cold cast iron skillet skin side down, giving them enough space to render their fat properly.Rinse off the salt on the eggplant in the colander over the sink. Take paper towels and squeeze as much moisture as you can from the eggplant, set aside.
Place your cast iron skillet with thighs over a burner set to medium heat. If you're using gas, you might want to start off on medium-low heat. The thighs should start gently sizzling and releasing fat and moisture after 4 to 5 minutes. If you see smoke, turn your heat down and make sure the skin isn't sticking to the pan. Start checking the fat side underneath at the 8 minute mark, don't try and force the skin up if it's sticking, be patient. The skin should be golden brown by the 10 minute mark. Flip thighs over skin side up and transfer to the middle rack of oven. Place an oven-safe meat thermometer probe in a thigh to track its temperature. (optional)
Cook your thighs for 15 to 20 minutes in the oven. An internal temperature of between 180 and 190 degrees Fahrenheit is ideal for the chicken thighs to convert their collagen into mouth watering gelatin. Remove from oven and set the thighs aside. Turn off oven. Place a towel or oven mitt over the hot handle of the cast iron pan.
Once the oven has cooled down a bit, place the cooked chicken thighs back in the oven to keep warm. Add onions to the cast iron skillet on a burner over medium low heat. Again, watch the hot handle of the skillet so you don't burn yourself. Cook onions till soft and translucent, 5 to 7 minutes.
Add the red peppers and cook for 5 minutes.
Add the diced eggplant and cook for 5 minutes
Add the tomatoes and thyme. Cook until everything in the skillet is soft, adding water if necessary. Cook for 10 to 15 minutes.
Place the chicken thighs over the top of the samfaina and serve. (Optional: Garnish with lemon slices and chopped parsley.)