If preparing in the oven, preheat oven to 350 degree F. Trim and peel the onion but leave the root intact. Cut a very thin sliver off of the root end if you need to level the onion so it will stand upright. Cut about a 1 inch core out of the top of the onion.
Peel garlic and cut into slivers. Stuff one clove into each onion. Place the onion onto a square of foil large enough to wrap around the onion and enclose the top. Double wrap if cooking on the grill.
Drizzle the top with balsamic vinegar, then place about 2 teaspoons of butter into the center of each onion. Season lightly with salt, pepper and Cajun seasoning.
Wrap each onion with one slice of thin bacon, then another slice, securing with a toothpick if needed.
Bring the sides of the foil up and twist the tops to seal. Place onto a hot grill or bake on a tray in a preheated 350 degree F oven for 1 hour. Carefully open the tops of the packets and return to the oven for 20 minutes to crisp up the bacon.
Serve as is in the packets, one per person, or use a spatula to remove onions to a serving platter, pouring the juices over the top. Enjoy!