Preheat oven to 450 degrees F. Coat a 12- x 16-inch rimmed baking sheet with nonstick cooking spray. Roll out the pizza crust dough and pat it down, shaping it so that it fits right up to the edges of the pan. Place the pan in the preheated oven and bake for 5 minutes. Remove from the oven
Meanwhile, coat a large frying pan with nonstick cooking spray. Cook the ground beef over MEDIUM heat, crushing it against the pan with a large spoon, until fully cooked. Drain as much of the grease from the pan as possible. Return the pan to the heat and season with the salt and pepper, to tastes. Add the onion, bell pepper, and minced garlic. Finally, add the BBQ sauce. Combine well and allow to simmer for about 5 minutes over LOW heat. Remove from heat.
Pour the pizza sauce on to the par-baked crust, spreading it to the edges with a pastry brush or the back of a spoon. Spoon the cooked beef mixture evenly over the top. Tear the slices of mozzarella into smaller pieces and place them evenly over the beef mixture. Sprinkle the cheddar cheese over the top.
Return to the oven and bake for an additional 15 minutes or until the cheeses are melted and edges of the crust are lightly browned. Remove from oven and allow to sit for 5 minutes before slicing and serving