Preheat your oven to 375°F. While it heats, combine smoked paprika, garlic powder, onion powder, kosher salt, white pepper, brown sugar, and cayenne pepper in a small bowl—this creates a balanced dry rub with smoky depth and subtle heat. Pat the pounded chicken breasts dry with paper towels, then rub them evenly on both sides with the avocado oil, which helps the spices adhere and promotes browning. Generously coat all surfaces with the spice mixture, working it in gently so it adheres well.
Lightly oil a baking dish (9x13 inches or similar) and place it in the preheated oven for 2 minutes to get it hot. Carefully transfer the seasoned chicken to the hot dish—you'll hear a gentle sizzle, which means the proteins are beginning to set and develop flavor. Immediately coat the top surface of the chicken with half of the BBQ sauce (about 1/2 cup), spreading it evenly. Place the dish in the oven and bake for 20 minutes without moving it.
After 20 minutes, carefully flip each chicken breast using tongs or a spatula—flipping partway through ensures both sides cook evenly and develop a nice caramelized coating. Spread the remaining BBQ sauce (about 1/2 cup) on the now-exposed top surface, coating generously. Return to the oven and bake for another 18-20 minutes. I like to check the internal temperature at 18 minutes with a meat thermometer inserted into the thickest part—once it reaches 165°F, the chicken is perfectly cooked and won't be dry.
Remove the baking dish from the oven and let the chicken rest for 5 minutes in the residual heat—this allows the juices to redistribute throughout the meat, keeping it tender and moist. Transfer to a serving plate, slice if desired, and drizzle any pan juices over the top for extra flavor and moisture.