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 portions. 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 2–3 minutes on one side, then flip and cook for an additional 2–3 minutes or until they reach an internal temperature of 160°F (71°C). Top each patty with a slice of American cheese and allow it to melt.
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 a patty, tomato slices, caramelized onions, and optional pickles. 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.