Prepare the vegetable patty by mixing 200 grams of boiled and mashed potatoes, 100 grams of grated carrots, 100 grams of finely chopped beans, 50 grams of boiled and mashed peas, 1/2 teaspoon of ginger-garlic paste, 1/2 teaspoon of garam masala, 1/2 teaspoon of red chili powder, salt to taste, and 2 tablespoons of cornflour. Mix well and form into 4 equal-sized patties.
Heat oil in a pan for shallow frying. Coat the vegetable patties with breadcrumbs and shallow fry them until they turn golden brown and crispy on both sides. Drain on a paper towel and set aside.
In a small bowl, mix 4 tablespoons of mayonnaise with 2 tablespoons of tomato ketchup to make the burger sauce.
Slice 4 burger buns horizontally and toast them lightly on a tawa or pan.
Assemble the burger by spreading the burger sauce on the bottom half of the bun, placing a lettuce leaf, followed by the crispy vegetable patty, a slice of tomato, a slice of onion, and a slice of cucumber. Spread some more burger sauce on the top half of the bun and place it on top of the assembled ingredients.