Make the onions: Heat the olive oil in a large skillet over medium-high heat until almost smoking. Add the onions and stir to coat. Reduce the heat to low and cook until the onions are golden, about 30 minutes. Remove from the heat and add the bourbon, scraping up any browned bits with a wooden spoon. Return to low heat, add the butter and cook until melted. Add the sugar, and salt and pepper to taste, and cook until there is very little liquid left.
Meanwhile, make the aioli: Pulse all of the ingredients in a food processor until combined. Cover and refrigerate until ready to use.
Make the sliders: Preheat a grill to medium high. Form the beef into twelve 4-ounce patties, about 1/2 inch thick. Oil the grill rack, then add the patties and season with the garlic salt, and sea salt and pepper to taste. Grill until browned and cooked halfway through, 3 to 4 minutes. Flip, top with some of the caramelized onions and cook 3 more minutes for medium (or to desired doneness).
Meanwhile, brush the insides of the buns with butter and toast on the grill, about 1 minute. Brush the insides of the bun tops with about 1 tablespoon aioli. Put the burgers on the bun bottoms and cover with the tops. Thread each lime wedge onto a skewer; pierce the skewers through the sliders.