In large zipper-lock plastic bag, combine salt, sugar, paprika, garlic cloves, and bay leaves. With rubber mallet or flat meat pounder, smash garlic into salt and spice mixture thoroughly. Pour mixture into large plastic container or nonreactive stockpot. Add 7 cups buttermilk and stir until salt is completely dissolved. Immerse chicken and refrigerate until fully seasoned, 2 to 3 hours.
Remove chicken from buttermilk brine and shake off excess; place in single layer on large wire rack set over rimmed baking sheet. Refrigerate uncovered for 2 hours. (After 2 hours, chicken can be covered with plastic wrap and refrigerated up to 6 hours longer.)
Measure flour into large shallow dish. Beat egg, baking powder, and baking soda in medium bowl; stir in remaining 1 cup buttermilk (mixture will bubble and foam). Working in batches of 3, drop chicken pieces in flour and shake pan to coat. Shake excess flour from each piece, then, using tongs, dip chicken pieces into egg mixture, turning to coat well and allowing excess to drip off. Coat chicken pieces with flour again, shake off excess, and return to wire rack.
Adjust oven rack to middle position, set second wire rack over second rimmed baking sheet, and place on oven rack; heat oven to 200 degrees F. Line large plate with double layer paper towels.
Meanwhile, heat oil (oil should have 2 1/2-inch depth in pan) to 375 degrees F over medium-high heat in large 8-quart cast-iron Dutch oven with a diameter of about 12 inches.
Place half of chicken pieces skin-side down in oil, cover, reduce heat to medium, and fry until deep golden brown, 6 to 8 minutes; after about 3 minutes, lift chicken pieces with tongs to check for even browning; rearrange if some pieces are browning faster than others. (Spot-check oil temperature; after first 6 minutes of frying, oil should be about 325 degrees. Adjust burner if necessary.)
Turn chicken pieces over and continue to fry, uncovered, until chicken pieces are deep golden brown on second side, 6 to 8 minutes longer. Using tongs, transfer chicken to paper towel-lined plate; let stand 2 minutes to drain, then transfer to rack in warm oven. Replace paper towelling on plate. Return oil to 375 degrees and fry remaining pieces, transferring pieces to paper towellined plate to drain, then transferring to wire rack with other chicken pieces. Cool chicken pieces on wire rack about 5 minutes and serve.