In a heavy bottom kadhai (or if you have use the kerala mud chatti), add all the vegetables along with just enough water to cover them. Bring to a boil and reduce the flame. Cook till all the vegetables are tender, stirring occasionally. Make sure you chop vegetables in the same size more or less.
While the vegetables are cooking grind all the ingredients of the paste together. Namely coconut, green chillies and cumin seeds. Keep aside
Once the vegetables are cooked, add the coconut paste to the vegetables and simmer for 4-5 minutes.
In a small tadka pan, heat coconut oil and add mustard seeds, urad dal and red chillies. Roast for 1 minute till the urad dal starts to brown. Add curry leaves and fry further for 2 minutes till the leaves are crisp and the dal nicely browned.
Pour on top of the avial and serve warm