Peel the potatoes and cut them into chunks. Boil in salted water until tender, about 15 minutes, until a fork slides in easily.
Drain the potatoes and mash them thoroughly with a potato masher until smooth and fluffy. Let them cool slightly so they’re comfortable to handle.
Finely chop your mixed vegetables—carrots, peas, and beans—until they are small and uniform. Mix these into the mashed potatoes evenly.
Add the cumin powder, coriander powder, and salt to the vegetable-potato mixture. Stir well so the spices are evenly distributed, and the aroma of warm spices begins to fill the air.
Sprinkle in the besan (gram flour) and knead the mixture gently until it just comes together. It should be firm enough to hold shape but not dry or sticky. Adjust with a little more flour or water if needed.
Shape the mixture into small, flat patties about 1.5 inches in diameter. Use your hands to press firmly so they hold their shape, then set them aside on a plate.
Heat 2-3 tablespoons of neutral oil in a frying pan over medium heat until shimmering and hot, about 180°C (356°F). You can test if the oil is ready by dropping in a small piece of mixture—if it sizzles immediately, it’s perfect.
Carefully place the patties into the hot oil, leaving space between each. Fry for about 3-4 minutes on one side until they turn a deep golden brown and become crispy, then flip gently with a spatula and cook the other side for another 3-4 minutes.
Once the cutlets are evenly golden and crispy, transfer them to a plate lined with paper towels to absorb excess oil. Let them rest for a couple of minutes to firm up.
Serve the vegetable cutlets hot, with your favorite chutney or yogurt on the side, and enjoy their crispy, flavorful crunch that brings back nostalgic memories.