For brine, in a resealable plastic bag set in a bowl mix the 3 cups buttermilk, the kosher salt, and sugar. Using a chef's knife, cut chicken breasts in half crosswise. Add all chicken pieces to the brine; seal bag. Chill for two -- four hours; remove chicken from brine. Drain chicken; pat dry with paper towels. Discard brine.
In a large bowl, mix flour, salt and pepper. Place the 3/4 cup buttermilk into shallow dish. Coat chicken with flour mixture, dip in the buttermilk, and coat again with flour mixture.
Meanwhile in a deep, heavy pot or a deep fat fryer heat 1 1/2 inches of oil to 350°. Using tongs, carefully add a few pieces of chicken to hot oil. Oil temperature will drop; maintain temperature at 325. Fry chicken for 12 to 15 minutes or until chicken is no longer pink and coating is Golden, turning once. Drain on a wire rack or paper towels. If desired, keep Fried chicken warm in a 300° oven while frying remaining chicken pieces. Makes six servings.
Note: spicy buttermilk brine fried chicken: prepare as directed, except add 1 1/2 teaspoons cayenne pepper to the flour mixture.