Prepare the sauce by mixing mayonnaise, ketchup, and mustard in a small bowl. Set aside.

Heat vegetable oil in a skillet over medium heat. Add diced onion and sauté for 5–7 minutes until golden and caramelized. Remove from heat.

Divide ground beef into two patties per portion, shaping slightly larger than the buns. Season both sides with salt and black pepper.

Heat a grill pan or skillet over medium-high heat. Cook the patties for 2–3 minutes on one side. Flip the patties, top each with a slice of American cheese, and cook for 1 minute longer or until the cheese melts.

Toast the hamburger buns, cut-side down, in a skillet or toaster until golden brown.

To assemble the burgers, spread the prepared sauce on the bottom bun. Layer shredded romaine lettuce, sliced tomato, the double-stacked patties, and caramelized onions. Top with the other half of the bun.

For the mango lassi, blend frozen mango, plain yogurt, milk, ground cardamom, and sugar until smooth. Adjust sweetness to taste.

Serve the burgers with the carrots and ranch dressing on the side.