Preheat a smoker to 250°F. Set it up for indirect cooking, and prepare a rimmed sheet pan or shallow smoker-safe pan for the meatloaf.
In a small bowl, stir together the BBQ sauce, balsamic vinegar, and Dijon mustard. Set this balsamic BBQ glaze aside.
In a large bowl, combine the ground beef, ground pork, breadcrumbs, egg, milk, onion, garlic, salt, black pepper, and smoked paprika. Mix gently with your hands until just combined.
In a separate bowl, mix the chopped spinach, sun-dried tomatoes, and shredded mozzarella. Set the filling aside.
Lay a large piece of parchment on the counter. Pat the meat mixture into a rectangle about ½ inch thick. Spread the spinach filling down the center, leaving a border around the edges. Use the parchment to bring the long sides of the meat over the filling, then pinch the seam and ends closed. Place the loaf seam-side down in the prepared pan.
Smoke the meatloaf until the center reaches 150°F, about 1½ to 2 hours depending on its shape and the smoker. Brush the top and sides with some of the balsamic BBQ glaze.
Continue smoking until the center reaches 160°F. Brush with the remaining glaze during the final 10 minutes, then remove the meatloaf from the smoker.
Rest the meatloaf for 10 minutes before slicing. Cut gently so the spinach, tomato, and cheese filling stays centered in each piece.