1. Place the lemon zest, basil, garlic, 1/2 teaspoon of the salt, 3/4 teaspoon of the pepper, and 2 tablespoons of the olive oil in the bowl of a food processor fitted with a steel blade and pulse until it forms a chunky paste.
2. U Place the chicken pieces in a large shallow glass or ceramic bowl and add the lemon and basil mixture. Cover and let sit at room temperature for no more than 1 hour, or refrigerate for at least 4 hours or overnight.
3. Combine the flour, the remaining kosher salt, and the rest of the pepper in a shallow bowl or plate and set it aside for dredging the chicken.
4. Heat a large skillet over medium-high heat and add 2 tablespoons of the olive oil. Remove the chicken from the marinade and dredge it in the flour mixture. Place the chicken directly in the hot oil.
5. Because cooking the chicken will take 2-3 batches, you may need to clean out the pan between batches with a paper towel and add more oil. If you are using a whole, cut-up chicken, cook it for about 10 minutes on the first side and about 7 on the second. If you are using boneless breasts, cook for about 5 minutes on the first side and 3 on the second.
6. Remove the chicken from the pan and place on paper towels.