Prepare Sauce: Mix mayonnaise, ketchup, and mustard in a small bowl. Set aside.
Caramelize Onions: Heat oil in a skillet over medium heat. Add onion and sauté for 5–7 minutes until golden and caramelized. Remove from heat.
Shape and Season Patties: Divide ground beef into even portions (2 patties per portion). Shape into patties slightly larger than the buns. Season with salt and black pepper.
Heat a grill pan or skillet over medium-high heat. Cook patties for 2–3 minutes on one side. Flip and top with cheese, cook until melted. Stack 2 patties per portion on top of one another.
Toast the bun halves, cut-side down, until golden.
Spread sauce on the bottom bun. Add the lettuce, tomato, patty stack, caramelized onions, and optional pickles. Top with the other bun half.
Prepare Mango Lassi: In a blender. Blend mango, yogurt, milk, cardamom, and sugar until smooth. Adjust sweetness to taste.
Serve: Plate burgers with carrots, ranch dressing, and mango lassi.