Heat the oven to 375°F. Lightly grease 8 cups of a standard muffin pan.
In a large bowl, combine the ground beef, breadcrumbs, egg, diced onion, 2 tablespoons of the BBQ sauce, Worcestershire sauce, smoked paprika, garlic powder, salt, and black pepper. Mix just until evenly combined.
Divide the mixture into 8 portions. Press each portion into a cup of the muffin pan, making a hollow in the center. Place one smoked mozzarella cube in each hollow, then cover it with the meat mixture and seal the top so the cheese is enclosed.
Brush the tops with the remaining BBQ sauce. Bake until the meat is cooked through, about 20 to 25 minutes. If checking with a thermometer, the center of a muffin should reach 160°F.
Let the muffins rest in the pan for 5 minutes before removing them. This gives the melted cheese a moment to settle and makes the muffins easier to lift out.