Prepare the Sauce: Mix mayonnaise, ketchup, and mustard in a small bowl. Set aside.
Caramelize the Onions: Heat vegetable oil in a skillet over medium heat. Add diced onions and sauté for 5–7 minutes until golden brown. Remove from heat.
Shape and Season the Patties: Divide the ground beef into 2 patties per portion. Shape each portion into a patty slightly larger than the hamburger buns. Season with salt and black pepper.
Cook the Patties: Heat a grill pan or skillet over medium-high heat. Cook patties for 1–2 minutes on one side, then flip and top with cheese, cook for an additional 1–2 minutes or until the cheese is melted. Stack 2 patties per portion on top of one another.
Toast the Buns: Toast hamburger buns cut-side down in a skillet or toaster until golden brown.
Assemble the Burgers: Spread the prepared sauce on the bottom half of each bun. Layer with lettuce, tomato slices, patty stack, and caramelized onions. Top with the other bun half.
Prepare the Mango Lassi: Blend frozen mango, yogurt, milk, cardamom, and sugar until smooth. Adjust sweetness to taste.
Serve: Plate the burgers alongside the carrots and ranch dressing. Serve the mango lassi in a glass on the side.