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 2 patties per portion. Shape into patties slightly larger than buns. Season with salt and black pepper.
Cook Patties: 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 1 minute longer or until melted. Toast Buns: Toast bun halves cut-side down until golden. Then stack 2 patties on top of one another per portion.
Assemble Burgers: Spread sauce on the bottom bun. Add lettuce, tomato, patty stack, and caramelized onions. Top with the other bun half.
Make Mango Lassi: Blend mango, yogurt, milk, cardamom, and sugar until smooth. Adjust sweetness to taste.
Serve: Plate burgers and serve with carrots, ranch, and mango lassi.