Season the chicken generously with salt and pepper. Place on a baking sheet and refrigerate, uncovered, 1 hour to infuse the flavor.
Whisk 3 cups buttermilk, the hot sauce and mustard in a large bowl. Stir in the garlic and onion slices, then the chicken. Cover and refrigerate 2 to 4 hours.
Whisk the flour, baking powder, paprika, onion powder, garlic powder, cayenne, 1 tablespoon salt and 2 teaspoons pepper in a large bowl. Drizzle in the remaining 1/3 cup buttermilk and whisk to form small shaggy clumps.
One piece at a time, remove the chicken from the buttermilk, letting any excess drip off, and coat in the flour mixture, pressing with your hands to coat well. Transfer to a rack set on a baking sheet.
Fill a large cast-iron skillet with 1 inch vegetable oil. Heat over medium heat until a deep-fry thermometer registers 350 degrees F. Carefully add 4 to 5 pieces chicken to the hot oil. The oil temperature will drop; adjust the heat as needed to maintain a temperature of 325 degrees F. Fry the chicken, without turning, until the crust starts browning, about 2 minutes. Flip the chicken and fry, turning occasionally, until browned and crisp all over and a thermometer inserted into the breasts registers 160 degrees F and the thighs 170 degrees F, 12 to 16 minutes. Remove with tongs to a clean rack set on a baking sheet; sprinkle lightly with salt. Let the oil temperature return to 350 degrees F before frying the remaining chicken.
After all the chicken is cooked, fry the onions, if desired: Drain the onions, separate the rings, then coat with the flour mixture. Fry, turning once, until crisp and golden brown, 2 to 3 minutes. Drain on paper towels and sprinkle with salt.
We used a big spoonful of baking powder in the coating for this Nashville-style chicken. It draws out moisture, so the skin gets extra crisp before it?s dipped in fiery cayenne-spiced butter.