Heat the oven to 375°F. Lightly grease 8 cups of a standard muffin tin.
Add the ground beef, egg, breadcrumbs, Parmesan, marinara, Italian seasoning, garlic powder, salt, and black pepper to a mixing bowl. Mix gently until just combined.
Divide the mixture into 8 portions. Press half of each portion into the bottom of a prepared muffin cup, making a small space in the center. Place one mozzarella cube in each space, then cover with the remaining meat mixture and seal the edges around the cheese.
Spoon the barbecue sauce over the tops of the muffins, spreading it into an even layer.
Bake until the muffins are browned and cooked through, about 25 to 30 minutes. Let them rest in the tin for 5 minutes before removing, so the melted mozzarella settles slightly.