In a large vessel, heat 3 cups of water with 1 tsp salt and turmeric. Add all the chopped veggies, bring to a simmer. Cover and cook until the carrot and potatoes are cooked.
In a kadai/wok, heat 1 tsp oil. Add all ingredients for spice paste, except coconut and fry on a low flame until chillies are bright red, rice is opaque and udad dal is golden brown. Place this in a small mixer and grind to a fine paste along with coconut and 1/2 cup water.
Mash the pressure cooked dal well with a ladle or whisk and add to cooked veggies.
Mix the cooked veggies (with the liquid), dal and spice paste in a saucepan and bring to a simmer.
In a tempering ladle or small wok, heat 2 tsp oil. Add mustard seeds. Once they splutter, add the curry leaves, udad dal. Wait for dal to turn golden brown, add pinch of asafoetida and transfer this over the vegetable dal spice mix.
Remove from stove and keep covered until ready to serve.
Serve with steamed rice and ghee along with a papad on the side.