Heat ghee in a heavy bottomed vessel, add mustard seeds and allow to splutter, add cumin seeds and let them brown. Add curry leaves and saute for few secs.
Add the carrot, potato and brinjal pieces and saute on medium flame for 3-4 mts. Reduce flame, add salt and turmeric pwd and combine. Place lid and cook till the vegetables are half cooked. Add tomatoes and cook further for another 4-5 mts.
While the vegetables are cooking, heat oil in a pan, add channa dal, coriander seeds, khus khus, cinnamon stick and red chilies and saute till the dals turn red and a lovely aroma emanates the kitchen. Add the coconut and asafoetida and roast for half a mt. Turn off heat and cool. Grind this mixture without water till it becomes a powder, add little water and make a smooth paste.
Add 2 1/2 cups of water to the vegetables and bring to a boil. Cook with lid for 7-8 mts. Remove lid and add the ground paste and combine well. Cook on low-medium flame for 15-20 mts, till the texture is thick and not watery.
Turn off heat and garnish with fresh coriander leaves.
Serve with hot rice, chapatis or dosas.