In a medium skillet heat the olive oil over medium heat. Add the sugar and red onions and cook for 15 minutes, stirring occasionally, or until the onion is caramelized.
Add in 3 tablespoons of bourbon, vinegar, and ½ teaspoon of salt. Cook for 2 minutes or until the liquid is almost evaporated. Remove mixture from heat and cool for 5 minutes.
In a small saucepan combine the remaining bourbon, ketchup, Dijon mustard, honey, Frank's Red Hot, 1 tablespoon of Worcestershire sauce, and black pepper. Bring to a boil, stirring frequently. Reduce heat and simmer for 10 minutes. Remove from heat.
In a large bowl combine the ground beef, remaining Worcestershire sauce, and breadcrumbs. Season with salt and pepper.
Divide the beef into 5 patties. Sprinkle with remaining salt.
Grill the burgers on a gas grill over medium heat for 4-5 minutes per side.
Place 1 tablespoon of BBQ sauce on the bottom of each bun and top with a lettuce leaf. Then place the burger on top of the lettuce. Place 1-2 tablespoons of the red onion mixture on top.