Place the grated carrots, mashed potatoes, thawed green peas, toasted cumin, coriander powder, paprika, chopped green chili, salt, and beaten egg in a large mixing bowl. Stir everything together until well combined, forming a cohesive mixture.
Add the toasted breadcrumbs to the mixture, mixing thoroughly. If the mixture feels too loose, sprinkle in a little more breadcrumbs until it holds shape easily.
Divide the mixture into 8-10 portions, shaping each into a round, flat patty about 1 cm thick. Gently press to ensure they hold together well.
Heat enough oil in your frying pan or deep fryer to cover the bottom by about 2-3 cm. Once the oil reaches 180°C (350°F) — test by dropping a small piece of bread, which should sizzle and turn golden in 30 seconds — carefully place the cutlets in the hot oil.
Fry the cutlets in batches, cooking for 3-4 minutes per side until they turn deep golden brown and crispy. Use a spatula or slotted spoon to flip them gently, hearing the sizzling and smelling the fragrant spices.
Once cooked, transfer the cutlets to a paper towel-lined plate or a wire rack to drain excess oil. Let them sit for a couple of minutes to crisp up further.
Serve the vegetable cutlets hot, garnished with fresh herbs or lemon wedges if desired. They should be crispy on the outside, tender inside, with a smoky, spicy aroma inviting you to take a bite.