Heat the oven to 375°F. Line a rimmed baking sheet with foil and set a wire rack on top.
In a large bowl, combine the ground beef, egg, breadcrumbs, onion, 2 tablespoons of the barbecue sauce, smoked paprika, garlic powder, salt, and black pepper. Mix gently until just combined.
Transfer the meat mixture to the prepared rack and shape it into a rectangle about 8 inches long. Place the smoked Gouda down the center. Fold the meat around the cheese and pinch the edges closed to seal it inside.
Lay the bacon slices across the loaf, slightly overlapping them. Tuck the ends underneath so the bacon stays in place as it cooks.
Stir the remaining 2 tablespoons of barbecue sauce with the brown sugar. Brush half of the glaze over the bacon-wrapped loaf.
Bake until the center reaches 160°F, about 55 to 65 minutes. Brush with the remaining glaze during the final 15 minutes. If the bacon needs more browning, broil briefly at the end, watching closely.
Let the meatloaf rest for 10 minutes before slicing. This gives the melted Gouda time to settle and helps the slices hold together.