Pat the chicken dry with paper towels and season the pieces with salt (about 3/4 teaspoon per pound) on both sides as soon as you get home from the market, if possible. When you are ready to cook them, pat dry again and allow them to sit at room temperature for about 30 minutes to take off some of the chill. Add them to a cold cast iron skillet, skin side down.
Turn the heat to medium and cook them without moving them for about 15 to 30 minutes, depending on the size of the pieces, until the skin is perfectly golden brown. You can use a splatter guard to prevent your stove from getting messy. Reduce the heat if the skin begins to burn before it gets evenly golden brown.
Turn the thighs over and continue cooking the thighs until the meat closest to the bone is cooked through, about 15 minutes more. Alternatively, after flipping the chicken, you can finish them in a 375 degree F oven for 15 minutes or until the meat reaches 165 degrees.
In the meantime, toss the herbs, shallot and chili pepper with half of the lemon juice and all of the olive oil. Plate the chicken and drizzle with the other half lemon juice and top with the herb salad plus a pinch of salt and pepper.