Cut the chicken quarters into drumsticks and thighs. Toss the chicken with 1 tablespoon salt and lay on a plate. Cover the chicken and chill overnight in the fridge.
Make the marinade. Whisk together 1 cup buttermilk with ¼ cup pickle brine, 1 egg, 2 Thai chiles, 1 teaspoon grated ginger, 1 tablespoon soy sauce, and 1 teaspoon ground white pepper. Add the chicken, stirring to coat. Marinate the chicken for 2-4 hours in the fridge.
Preheat the oven to 425 degrees F.
Remove the chicken from the marinade, scraping off any extra buttermilk mixture. Coat the chicken in flour, shaking off the excess. Let the chicken rest for 10 minutes to dry out the coating.
Pour ¼ cup oil into a baking sheet and preheat in the oven for 10 minutes. Carefully lay the chicken on the baking sheet with the hot oil and drizzle another 2 tablespoon oil directly on the chicken. Oven-fry the chicken for 30 minutes or until browned and the juices run clear.
Meanwhile, make the spiced butter. Combine ½ cup melted butter with 1 tablespoon Szechuan peppercorns, 1 tablespoon Korean chile flakes, 1 tablespoon brown sugar, 1 tablespoon sesame oil, 1 teaspoon Chinese five-spice, 1 teaspoon salt, ½ teaspoon ground white pepper, ½ teaspoon cumin, ½ teaspoon garlic powder, ¼ teaspoon coriander, and ¼ teaspoon ginger. Brush the sauce on the chicken, making sure to coat both sides. Serve immediately.