Whisk the buttermilk, hot sauce and 1 teaspoon salt, add the chicken and refrigerate for 4 to 12 hours.
Combine the flour, garlic powder and remaining salt in a wide bowl, then press each drained thigh into the dredge twice for a compact, even shell.
Rest the coated chicken on a rack for 10 minutes while heating the peanut oil in a deep heavy pot to 350°F.
Fry 2 thighs at a time for 6 to 8 minutes, turning once and maintaining 335°F to 350°F, until deep gold and 165°F inside.
Drain the chicken on a wire rack and carefully measure 1/3 cup hot frying oil into a heatproof bowl.
Whisk the cayenne, brown sugar and paprika into the measured oil, then brush the hot mixture over both sides of every fried thigh.
Toast the buns lightly and assemble each with 1 hot chicken thigh and 4 pickle chips.