In a large skillet, on a couple of tbsp of oil saute onion until soft and tender, about 3-5 minutes. Add cider vinegar and brown sugar, stirring occasionally, until the mixture becomes thick.
Combine the mayo and garlic in a small cup and set aside in the fridge.
Add a drizzle of olive oil to a large skillet and heat over MED-HIGH heat. Add hamburger buns, cut side down, and toast until golden brown. Turn off heat and remove to a plate to cool.
In a large mixing bowl, add ground beef, heavy cream, and spices. Use your hands to mix gently until just combined. Form into 4 patties.
Heat a drizzle of oil in the same skillet over MED heat and cook burgers about 5 minutes per side, or until cooked to desired doneness.
At the last-minute of cooking, place cheese slices on patties and cover the pan with aluminum foil. Serve hamburgers on toasted buns with lettuce, tomato, bacon, barbecue sauce, aioli, and caramelized onions.