Cut carrot, potato, and drumstick into long, uniform thick batons.
Boil vegetables in water with turmeric powder and salt until tender yet firm.
Coarsely grind grated coconut, green chilies, and cumin seeds without adding extra water.
Add coconut paste to the cooked vegetables, simmer for 3 minutes.
Turn off heat, stir in beaten yogurt, fresh curry leaves, and a generous drizzle of raw coconut oil before serving.