In a small bowl, combine the mayo, ketchup, and paprika. Cover and chill until ready to serve.
Cook the bacon, onion, and garlic in a skillet over medium heat. Set aside to cool (reserve the bacon fat). When cooled, combine ground beef, bacon, drippings, lime juice, cilantro, salt and pepper. Form into 1/4" thick patties, cover, and place in fridge for at least 30 minutes to 1 hour.
Preheat a skillet or griddle to medium-high heat. Cook patties 5 to 7 minutes, flipping once. Lay sliced cheese over patty when almost done and cover to steam and melt.
Serve on toasted bread with mayo-ketchup sauce, avocado, lettuce, tomato and other desired toppings.