Peel and grate the potatoes using a coarse grater, then place them in a large mixing bowl.
Add the chopped or grated mixed vegetables, chopped cilantro, garam masala, cumin, and chili powder to the bowl with potatoes. Mix thoroughly until well combined.
Gradually sprinkle in the chickpea flour, mixing as you go, until the mixture holds together when pressed but isn't sticky. If it feels too wet, add a little more chickpea flour.
Divide the mixture into 8 equal portions, then shape each into a flat, round patty about half an inch thick. Keep your hands damp to prevent sticking.
Heat about half an inch of oil in a frying pan over medium heat until shimmering and hot, around 180°C (350°F).
Carefully place the patties into the hot oil, frying in batches. Cook for about 3-4 minutes on each side until golden brown and crispy, listening for a gentle crackle.
Use a spatula to flip the cutlets gently, ensuring even browning. Once golden and crispy, transfer them to paper towels to drain excess oil.
Repeat frying the remaining patties, adjusting heat as needed to prevent burning.
Let the cutlets rest for 2 minutes to firm up the crust, then serve hot with chutney or yogurt, or let cool for a crispy snack later.