Brine. Whisk the buttermilk, salt and hot sauce in a large bowl or zip-top bag. Add the chicken, turn to coat, cover and refrigerate for at least 4 hours and up to 12 hours.
Mix the seasoned flour. In a wide, shallow dish, whisk together the flour, cornstarch, baking powder, paprika, garlic powder, onion powder, salt, black pepper and cayenne. Set a wire rack inside a rimmed baking sheet next to it.
Double dredge. Lift one piece from the buttermilk, let the excess drip off and press it into the flour on all sides. Dip it back into the buttermilk for a second, then press it into the flour again until it looks shaggy and fully covered. Set it on the rack and repeat with the rest.
Rest the coating. Leave the pieces on the rack for 15 to 20 minutes. The flour turns slightly damp and paste-like in spots, which means it will cling in the oil instead of sliding off.
Heat the oil. Pour the oil into a 12-inch cast iron skillet with sides at least 2 inches tall; it should never come more than halfway up the sides. Clip a deep-fry thermometer to the pan and heat over medium to medium-high until it reads 350°F (175°C), about 10 to 15 minutes.
Fry the dark meat. Gently lay the thighs and drumsticks in the oil skin side down, thighs toward the center, without crowding. The temperature will drop to around 300°F; adjust the burner so it stays between 300°F and 325°F (150-165°C). Fry until the underside is deep golden brown, 6 to 7 minutes, then turn with tongs and fry 6 to 7 minutes more.
Check the temperature. Insert an instant-read thermometer into the thickest part of each piece without touching the bone. Thighs and drumsticks must read at least 165°F (74°C); 175°F (79°C) gives the most tender dark meat. Transfer finished pieces to the clean wire rack.
Fry the white meat. Bring the oil back to 350°F, then add the breast pieces and wings and hold the oil at 300-325°F again. Fry the breast pieces 5 to 6 minutes per side and the wings 4 to 5 minutes per side, until deep golden and at least 165°F (74°C) in the thickest part.
Finish in the oven if needed. If any piece is deep brown outside but still under 165°F, move it on the rack and baking sheet to a 350°F (175°C) oven for 5 to 10 minutes and check again.
Rest and serve. Let the chicken rest on the rack for 10 minutes so the crust sets and the juices settle. Serve hot or at room temperature.