Cook the bacon in a large skillet over medium heat. Remove and drain on paper towels. Pour out the bacon grease, leaving the skillet unwashed. Heat olive oil in the same skillet. Add the sliced onions and cook until browned and tender, stirring occasionally.

Add 3 tablespoons bourbon and the balsamic vinegar to the onions. Cook for about 2 minutes until most of the liquid has evaporated. Remove from the skillet and allow the mixture to cool for 5 minutes.

In a small saucepan, combine the remaining 2 tablespoons bourbon, ketchup, Dijon mustard, honey, Worcestershire sauce, smoked paprika, and garlic powder. Bring the sauce to a boil, then reduce to a simmer. Cook for about 5 minutes, stirring frequently, until thickened. Remove from heat.

Coarsely chop about one quarter of the cooled onion mixture and mix it into the ground beef. Divide the beef mixture into 4 equal portions and shape into ½-inch-thick patties. Press a thumb-sized indentation into the center of each patty. Season with salt and pepper.

Preheat a grill to medium-high heat and lightly oil the grates. Grill the patties for approximately 4 minutes per side, or until they reach your preferred level of doneness.

To assemble, spread the bourbon sauce generously on both halves of each bun. Place a burger patty on the bottom bun, followed by a slice of cheese if using, a portion of the remaining onion mixture, and one slice of bacon cut in half. Top with the remaining bun.Serve immediately and enjoy.