Directions
For the chicken, combine 1/2 cup flour, parsley, 1 tsp. thyme, 1 tsp. pepper and salt in a shallow dish. Place buttermilk in a second shallow dish. Dredge chicken in flour mixture, dip in buttermilk, then dredge again in flour mixture. Cool coated breasts on a rack placed on a baking sheet for at least 5 minutes.
Heat 1/4 inch oil in a medium saucepan until shimmering. Fry chicken until golden on one side, about 6 minutes. Flip the chicken and fry until brown and cooked through, 5-6 minutes more. Transfer chicken to a plate and tent with foil. Pour in all but 1 c. oil.
For pepper sauce, cook garlic in same pan over medium-high heat until fragrant, about 1 minute. Whisk in 3 c. flour and 1 1/2 tsp. pepper; whisk slowly into milk. Boil sauce, whisking constantly, until thick, 2-3 minutes. Stir in 1 tsp. thyme and salt.
Serve gravy over chicken.