Preheat the oven to 350 degrees F. Place the brown sugar in a pie dish. Gently press each slice of bacon into the sugar until coated (there can be small patches of uncoated bacon). Line a baking sheet with a wire rack and spray with cooking spray. Arrange the bacon on the rack. Bake, rotating the pan halfway through baking, until the bacon is super crisp and golden, 30 to 50 minutes (depending on the thickness of the bacon). Remove the rack from the pan and let the bacon cool on the rack.
Meanwhile, heat a large skillet over medium heat. Place the vegetable oil and onions in the pan and gently cook, stirring only occasionally to let the sugars develop, until the onions are a deep golden brown, about 30 minutes. If necessary, deglaze the pan with red wine a couple of times. Season with the vinegar, salt and pepper and set aside.
Combine the mayonnaise, barbecue rub and hot sauce in a small bowl to make an aioli.
Build the sandwiches: Season the tomato slices with salt; cut the bacon slices in half. On each toasted bun, place a layer of caramelized onions, followed by about 6 half slices of bacon, a tomato slice, a romaine leaf and a nice schmear of the aioli on the bun top only. Close and serve with extra aioli on the side.