Heat the oven to 375°F. Grease 8 cups of a standard muffin pan.
Cook the macaroni according to the package directions until just tender. Drain it, then return it to the pot. Stir in the butter and milk until the butter melts. Add ½ cup of the cheddar and stir until creamy. Set the macaroni and cheese aside.
In a mixing bowl, combine the ground beef, breadcrumbs, egg, diced onion, garlic powder, smoked paprika, salt, pepper, and ¼ cup of the barbecue sauce. Mix gently until just combined.
Divide about two-thirds of the beef mixture among the 8 greased muffin cups. Press it across the bottom and up the sides of each cup to make a small well.
Spoon the macaroni and cheese into the wells, dividing it evenly. Cover the filling with the remaining beef mixture and gently seal the edges so the centers are enclosed.
Brush the tops with the remaining ¼ cup barbecue sauce. Bake until the meat is cooked through, about 20 to 25 minutes. Let the muffins rest in the pan for 5 minutes before carefully lifting them out.