To a large bowl add the chicken, salt, and pepper. Mix to coat the chicken. Cover and chill for at least 6 hours to overnight.
Make the marinade by whisking together the buttermilk, eggs, and hot sauce in a mixing bowl. Pour the marinade over the chicken and mix until thoroughly coated. Chill for another 3 hours.
Blot the chicken with paper towels to remove any excess marinade and set chicken aside on a plate. Place a wire rack over a baking sheet and set aside.
In a shallow dish (like a pie plate) mix the flour, salt, and cayenne. Coat all sides of the chicken in the flour mixture. Then set it on the wire rack to drip dry for about 20 minutes.
In the meantime, make the sauce by melting together the butter, chili powder, brown sugar, garlic powder, and paprika in a medium saucepan over medium heat. Cook until the sugar dissolves and then remove from the heat.
Place a deep-sided pan or large pot over medium-high heat and pour in 4 cups of vegetable oil. Test the oil's heat by throwing in a pinch of flour. If it sizzles immediately the oil is hot enough for the chicken (roughly 350 degrees F). Place the chicken in the hot oil and cook until about 8-10 minutes per side.
Transfer chicken to a wire rack over a baking sheet lined with paper towels to allow any excess oil to drip off and the chicken to cool slightly.
Warm the sauce back up and brush generously onto the chicken. Serve warm with white bread and pickles.