In a large bowl whisk together 1-3/4 cups buttermilk, 1/2-tablespoon salt, 1/2-tablespoon pepper. Divide the buttermilk mixture between two zipper freezer bags, and add 1 cut-up fryer to each bag. Seal the bag, removing as much as possible. Shake the bags to evenly coat the chicken. Refrigerate 2 hours, up to 2 days.
In a large shallow bowl combine flour, garlic, thyme, paprika, cayenne and remaining salt and pepper. Stir together to combine. Add 1/4-cup buttermilk and whole milk, and stir into flour until small lumps are formed.
Heat 4 cups of oil in a deep skillet or Dutch oven over medium high heat to 375 F.
Working in batches, remove chicken pieces from bag, shake off excess buttermilk. Dredge in flour and set on a wire rack to rest 10 minutes. Continue until all chicken has been coated once. When oil reaches 375 F, re-dredge chicken in seasoned flour and add to the preheated oil, 3 to 4 pieces at a time. Cover and fry 5 to 7 minutes. Remove lid, turn, and cook uncovered and additional 5 to 7 minute. Monitor the temperature of the oil, adjusting the heat to keep the oil between 360 F and 375 F.
Once cooked through and golden brown, remove from oil and place on a wire rack. Note: To keep chicken hot and crisp, keep cooked chicken on in a 200 F oven on a wire rack sitting in a rimmed baking sheet.
Continue as above with remaining chicken until all the chicken is cooked. Serve hot. Makes 6 to 8 servings.