Add the chopped carrot and peeled shallots in a cooking vessel along with one or two cups of water. Cook the vegetables in medium flame till they turn soft and delicate.
Till the time vegetables are cooking, proceed to roasting spices. Heat a wok or kadai adding oil. Include red chillies, asafoetida and coriander seeds. Saute them together and roast till the coriander seed's color deepen a bit.
Then include both the lentils and stir till they turn slightly brown. Continue adding pepper corns, raw rice, fenugreek seeds and curry leaves to the same wok. Stir for some time. Finally include grated coconut, green chilly, cinnamon and chopped tomato one after the other. Switch off once they are warm.
Transfer all the roasted ingredients in to a blender or mixer and grind to smooth paste. As the masala for sambar is ready, check the vegetables for done-ness. Add tamarind extract and jaggery at this stage.
Add the ground masala to the vegetables that are cooked. Combine well and include enough water to obtain the idli sambar consistency. Add required salt and bring it to boil. Let the sambar boil for 3 minutes. Garnish with some chopped coriander leaves.
Aromatic and drool-worthy tiffin sambar or Idli sambar is ready. Serve it with any tiffin like idli, dosa and uttappam.