Marinate the chicken: combine the chicken pieces with 1 cup buttermilk, 1 tsp salt, and 1/2 tsp black pepper in a bowl and refrigerate for at least 30 minutes or up to 2 hours.
Prepare breading: in a shallow bowl whisk together 1 cup all-purpose flour, paprika, garlic powder, onion powder, and cayenne (if using). Beat the eggs in a separate bowl.
Dredge chicken: remove chicken from marinade, shake off excess, dip each piece into eggs, then coat thoroughly in the seasoned flour. Set aside on a plate.
Fry chicken: heat 1/4 cup vegetable oil in a skillet over medium-high heat. Fry the coated chicken until golden brown and cooked through, about 3–5 minutes per side depending on thickness. Drain on paper towels.
Make biscuit dough: preheat oven to 425°F (220°C). In a bowl, combine 2 cups self-rising flour (or 2 cups all-purpose flour plus 3 tsp baking powder and 1/2 tsp salt), 1 tbsp sugar, and 1/2 tsp salt. Cut in 1/2 cup cold cubed butter until mixture resembles coarse crumbs.
Add milk and stir until just combined; do not overmix. Turn dough onto a lightly floured surface, gently pat or roll to about 3/4-inch thickness, and cut into rounds.
Bake biscuits: place rounds on a baking sheet and bake for 10–12 minutes until golden brown. Remove and let cool slightly.
Assemble sandwiches: split warm biscuits, place a piece of fried chicken inside each, and serve immediately.