Preheat the oven to 400˚F (200˚C). Prepare a 9-inch (22 cm) round cake pan with a 3½- inch (8 cm) ramekin in the center and set nearby.
Melt the butter in a large pan over medium-low heat. Add the onion and sauté until caramelized, stirring occasionally for about 15 minutes. Remove the pan from the heat.
Take a golf ball-sized piece of pizza dough and flatten it out with your fingers. Stuff the dough with about a teaspoon of caramelized onions and cooked bacon. Close the dough ball by pinching at the seam and roll into a ball in your hands. Repeat with the remaining dough and fillings.
Dip each stuffed ball in the melted butter. Place the stuffed balls in the prepared cake pan, stacking them around the ramekin.
Bake for 30 minutes, or until golden brown. Remove from the oven and reduce the oven temperature to 350˚F (180°C). Remove the ramekin with tongs (it will be hot!).
Place the wheel of brie in the center. Return the pan to the oven for 10 minutes more, or until the brie is soft.
Brush the monkey bread with more melted butter and sprinkle the bread and cheese with chives. Serve with vegetables like broccoli, potatoes, and mushrooms for dipping.