4 (5- to 7-ounce) bone-in chicken thighs, trimmed, or 2 (10- to 12-ounce) bone-in split chicken breasts, trimmed and halved crosswise
Salt and pepper
1 ¼ cups all-purpose flour
1 teaspoon baking powder
1 teaspoon garlic powder
½ teaspoon dried thyme
¼ teaspoon cayenne pepper
½ cup buttermilk
1 ½ cups peanut or vegetable oil
Season chicken with 2 teaspoons salt and 1/2 teaspoon pepper. Combine flour, baking powder, garlic powder, thyme, cayenne, 2 teaspoons salt, and 1 teaspoon pepper in shallow dish. Add 2 tablespoons buttermilk to flour mixture and rub together with your fingers until liquid is incorporated and shaggy pieces form. Place remaining 6 tablespoons buttermilk in second shallow dish.
Set wire rack inside rimmed baking sheet. Working with 1 piece at a time, dip chicken in buttermilk to thoroughly coat, letting excess drip back into dish; then dredge chicken in flour mixture, pressing to adhere. Transfer chicken to prepared wire rack. Refrigerate for 30 minutes to 1 hour.
Line large plate with paper towels. Add oil to 10-inch skillet until it measures about 1/2 inch deep and heat over medium heat to 350 degrees. Add chicken to hot oil, skin side down. Cover and fry until deep golden brown, 6 to 8 minutes, checking for even browning and rearranging pieces as needed halfway through frying. Adjust burner, if necessary, to maintain oil temperature around 300 degrees.
Turn chicken pieces over and continue to fry, uncovered, until chicken is deep golden brown on second side and thighs register 175 degrees or breasts register 160 degrees, 6 to 10 minutes longer. Transfer chicken to prepared plate and let cool for 5 minutes, flipping once to evenly blot away oil. Serve.