On a clean, floured surface, gently flatten a ball of dough with your hands until it is about 8” in diameter (or roughly smaller than your air fryer basket). Repeat with a second dough ball. Brush both with olive oil and transfer one, oil side up, into the basket of your air fryer.
In a medium bowl, stir to combine crushed tomatoes, BBQ sauce, garlic, and oregano, and season with salt and pepper. Spoon half tomato mixture onto the center of rolled out pizza dough, then spread into an even layer, leaving ½” outer crust bare.
Add half the mozzarella slices to the pizza. Air fry on 400° for 10 to 12 minutes, or until the crust is golden and the cheese is melted.
Remove the first pizza from the air fryer basket using 2 pairs of tongs, and garnish with basil leaves. Assemble and cook a second pizza, garnish, and serve.