Preheat the oven to 375°F and line a baking sheet with parchment paper.
In a large bowl, combine the ground beef, half the crumbled bacon, 1/4 cup BBQ sauce, breadcrumbs, egg, onion, smoked paprika, salt, and black pepper. Mix until evenly blended.
Divide the mixture into four equal portions. Press one cube of smoked Gouda into the center of each portion and shape the meat around it to fully enclose the cheese, forming small loaves.
Place the loaves on the prepared baking sheet. Brush the tops with the remaining 1/4 cup BBQ sauce and sprinkle with the rest of the crumbled bacon.
Bake for 25 to 30 minutes until the meat reaches 160°F inside and the cheese has melted.