Boil diced potatoes in 1 cup water with salt until fork tender.
Heat coconut or vegetable oil in a pot, add cinnamon stick, sliced onions, ginger paste, slit green chilies, and curry leaves.
Sauté gently until onions soften without browning.
Add cooked potatoes with water and thin coconut milk; simmer for 5 minutes.
Stir in thick coconut milk and black pepper, heat through without boiling, and serve warm with appam.