Soak 200 grams of urad dal (split black gram) in water for 4-5 hours. Drain the water and grind the dal into a smooth paste, adding a little water if required. Add salt to taste and mix well. Set aside.
Heat oil in a deep frying pan for deep frying the vadas. Wet your hands, take a small portion of the urad dal paste, shape it into a round disc, and make a hole in the center. Gently slide the vada into the hot oil and deep fry until golden brown. Repeat with the remaining paste. Drain the vadas on paper towels and set aside.
To prepare the sambar, cook 100 grams of toor dal (split pigeon peas) with 500 ml of water, 1/4 teaspoon turmeric powder, and a pinch of asafoetida in a pressure cooker for 3-4 whistles. Mash the cooked dal and set aside.
Heat 2 tablespoons of oil in a pan, add 1 teaspoon mustard seeds, 1/2 teaspoon cumin seeds, and a pinch of asafoetida. Once the seeds start to splutter, add 1 chopped onion, 2 chopped tomatoes, 1 chopped green chili, and a few curry leaves. Sauté until the onions turn translucent.
Add 1 tablespoon of sambar powder, 1/4 teaspoon turmeric powder, and salt to taste. Mix well and cook for 2-3 minutes.
Add the mashed toor dal, 500 ml of water, and a small piece of tamarind soaked in water (discard the pulp). Bring the sambar to a boil, then reduce the heat and simmer for 10-15 minutes.
To serve, place the fried vadas in a serving dish and pour the hot sambar over them. Garnish with chopped coriander leaves and serve with coconut chutney.