1. In a large bowl, whisk buttermilk with 1 Tbsp. salt and 1 tsp. pepper, mixing until salt has dissolved. Pat chicken pieces dry, cut off and discard wing tips and place chicken in bowl with buttermilk mixture. Cover and refrigerate for at least 12 hours or up to 1 day, turning chicken occasionally. (Alternatively, place half of buttermilk mixture and half of chicken in each of 2 large ziplock bags, seal, shake to coat and refrigerate.)
2. Place 2 wire racks on 2 large baking sheets. Whisk together flour, cornstarch, paprika, 1 tsp. salt and 1/2 tsp. pepper and divide flour mixture between 2 large ziplock bags. Working with a few pieces at a time, remove chicken from buttermilk mixture, letting any excess drip off. Drop chicken into flour mixture, seal bag and shake thoroughly to coat. Remove chicken pieces, shake off excess flour and place on racks. Repeat until all chicken pieces are coated. Let chicken rest on rack for 30 minutes to come to room temperature.
3. In a 12-inch cast-iron skillet or heavy frying pan, add 1/2 inch oil. Warm oil over medium-high heat until a deep-fry thermometer registers 350ºF.
4. Working in batches and using tongs, carefully place several chicken pieces skin-side down in the oil (do not crowd skillet). Cover skillet and cook chicken for 7 minutes. Uncover and turn chicken pieces over with tongs. Cook uncovered for 7 minutes, then turn again and cook until golden brown all over and cooked through, turning often, 5 to 7 minutes longer. (A meat thermometer inserted into thickest part should read 160ºF for white meat and 165ºF for dark.) Remove chicken to a clean wire rack to drain. Serve warm or at room temperature.