Whisk all spice rub seasonings together in a small bowl. Remove 1½ tablespoons spice rub to a large bowl and combine with 2 cups buttermilk and bay leaves.
Add chicken pieces to buttermilk mixture, toss to coat completely. Cover and refrigerate for 3 hours up to overnight.
Remove 1 teaspoon spice rub to a medium bowl for Nashville hot sauce. Stir in hot sauce, cayenne pepper, brown sugar, smoked paprika, and vegetable oil (mixture will be separated at this point).
Prepare buttermilk egg wash by whisking eggs, 1 cup buttermilk, and ¼ cup hot sauce in a medium bowl.
Prepare flour breading by whisking flour, baking powder, and all remaining spice rub seasonings in a large bowl.
Working with one piece at a time, dredge chicken in flour, shake off excess, coat in egg wash, shake off excess, then dredge again in flour. Place on baking rack.
Heat 3 inches of vegetable oil in Dutch oven to 375°F over medium-high heat.
Fry 3-4 chicken pieces at a time in single layer. Cover and cook 7 minutes, flip, cover and continue frying until internal temperature reaches 160°F (165°F for dark meat), about 5-7 minutes more.
Remove fried chicken to paper towel-lined baking sheet. Repeat with remaining pieces.
Vigorously whisk melted butter into Nashville hot sauce until smooth and combined.
Let chicken cool slightly, then brush with desired amount of hot sauce before serving.