Heat the oven to 375°F. Lightly grease eight cups of a standard muffin tin.
Add the sweet potatoes to a saucepan and cover them with water. Bring to a boil, then simmer until the chunks are tender when pierced with a fork, about 15 to 20 minutes.
While the potatoes cook, combine the ground beef, egg, oats, diced onion, 2 tablespoons of the barbecue sauce, garlic powder, smoked paprika, salt, and black pepper in a bowl. Mix gently until just combined.
Divide the beef mixture among the eight prepared muffin cups. Press it in lightly, leaving the tops rounded rather than packing the mixture tightly.
Bake for 15 minutes. Spoon the remaining 2 tablespoons of barbecue sauce over the muffins, then bake for another 8 to 12 minutes, until cooked through.
Drain the sweet potatoes well. Mash them with the butter, milk, and ¼ teaspoon salt until creamy. Serve the mash with the BBQ meatloaf muffins.