Peel and chop the ash gourd. Boil it with a little salt and water until softened, taking care not to overcook it.
Grind the coconut, mustard seeds, tamarind and green chillies to a smooth paste, adding water as needed.
Add the paste to the cooked ash gourd. Bring to a boil, then simmer for a few minutes. Check and adjust the seasoning.
For the nesal, heat the coconut oil in a small pan. Add the mustard seeds. Once they begin popping, add the urad dal, followed by the curry leaves. Pour over the cooked curry.
Mix and serve with warm rice.
If adding yogurt, wait around 5 minutes after switching off the heat. Whisk room-temperature yogurt and mix it separately into the portion being served. Avoid reheating that portion after the yogurt is added.