Grate the carrots into a large mixing bowl, then squeeze out any excess moisture to prevent sogginess.
Add the mashed potatoes and mashed green peas to the bowl with the grated carrots, mixing well to combine.
Toast cumin seeds in a small pan until fragrant, then grind or crush slightly before adding to the vegetable mixture.
Stir in the toasted cumin, coriander powder, garam masala (if using), chopped cilantro, and the flour or breadcrumbs. Mix until everything is evenly incorporated, and the mixture holds together when pressed.
Shape the mixture into small, flat patties about 2 cm thick and 8 cm wide, placing them on a plate as you go.
Heat oil in a wide skillet over medium heat until shimmering and lightly crackling when tested with a small veggie piece.
Carefully place the tikkis in the hot oil, leaving space between each. Fry for about 3-4 minutes until golden brown underneath, then flip and fry the other side for another 3-4 minutes until crispy and deep golden.
Once crispy and golden, transfer the tikkis to a paper towel-lined plate to drain excess oil. Continue frying remaining patties in batches.
Let the tikkis rest for 2 minutes to set their structure, then serve hot with chutney or yogurt, garnished with extra herbs if desired.