Preheat a smoker to 250°F. In a large bowl, combine the ground beef, breadcrumbs, egg, milk, Worcestershire sauce, salt, black pepper, smoked paprika, and ¼ cup of the barbecue sauce. Mix gently until just combined.

Shape the mixture into a loaf and place it on a smoker-safe tray or directly on the smoker grate. Smoke until the center reaches 160°F, about 2 to 3 hours depending on the loaf’s shape and the smoker. Brush the remaining ¼ cup barbecue sauce over the top during the last 20 minutes.

While the meatloaf smokes, heat the olive oil in a large skillet over medium-low heat. Add the sliced onions and cook, stirring occasionally, until soft and deeply golden, about 30 to 40 minutes. Lower the heat if they begin to brown too quickly.

Remove the meatloaf from the smoker and let it rest for 10 minutes. Slice it into four thick portions.

Place a slice of provolone on each meatloaf portion. Put the portions in a warm oven or under a broiler just until the cheese melts.

Toast the cut sides of the rolls until golden. Add a cheesy meatloaf portion to each roll and top with caramelized onions. Serve while warm.