Wash a 3 1/2-pound chicken and cut it into 8 pieces. Place in a nonreactive pan and add 1 quart buttermilk. Cover and refrigerate for at least 2 hours or as long as overnight. Combine 3 cups flour, 2 teaspoons paprika, 1 teaspoon cayenne pepper, 2 teaspoons salt, and 1 teaspoon freshly ground black pepper in a large plastic bag, and shake to mix. Heat 3/4-inch peanut oil in a cast-iron skillet over medium-high heat. Meanwhile, shake each piece of chicken in bag of seasoned flour until well coated. When oil is very hot but not smoking, add chicken, largest pieces first, skin side down. (Work in batches if your skillet is small.) Reduce heat to medium, and cook, turning once, until chicken is golden brown and crispy, 12-15 minutes per side. Drain chicken on paper towels.