Preheat the oven to 425 degrees.
Combine the beef, egg, and breadcrumbs in a bowl. Section into four equal portions.
Halve and peel the onions, and remove the root and tip ends. Peel off the two outer layers of the onions; reserve the rest for another use. Keep the onion layer halves together so that you don't mix them up.
Carefully stuff one onion half with half of a portion of meat mixture. Place a cube of cheese in the center, then mound the rest of the meat on top, to make a meatball. Press the matching onion layer onto the other side, so that your meatball is wrapped in onion.
Do the same for all of the meat and onions.
Wrap each meatball with three slices of bacon. Use toothpicks to secure it.
Bake the meatballs for 40-45 minutes. Brush with barbecue sauce, bake an additional 5 minutes, and remove from the oven. Remove the toothpicks and allow to cool at least 10 minutes before serving.