Peel the garlic cloves. Add garlic, ginger, onion, coriander seeds, cumin seeds, and black pepper to a mortar and pestle. Crush coarsely. You can also pulse briefly in a mixer grinder.
Heat oil in a kadai. Add mustard seeds and let them splutter. Add urad dal, dry red chillies, hing, curry leaves, and methi dana. Fry for 30 seconds.
Add the crushed masala. Cook on low flame for 1 minute until the raw smell of garlic goes away.
Add chopped tomatoes, coriander leaves, and salt. Cook until tomatoes soften.
Add tamarind pulp and Kashmiri red chilli powder. Bring to a boil.
Add cooked toor dal and enough hot water to reach your desired consistency.
Add coriander leaves, curry leaves, green chilli, and jaggery. Let the rasam come to one boil.
Switch off the flame and rest for 30 minutes before serving.
Make the Vada
Wash the soaked urad dal 4 to 5 times. Drain completely.
Grind the dal in pulse mode without water first. Add chilled water gradually and grind to a coarse batter.
Transfer batter to a bowl. Whip in one direction for 2 to 3 minutes until light. Test by dropping a small piece in water. It should float.
Heat oil in a kadai on medium heat. Wet your hands, take small portions of batter, and drop gently into the oil. Fry 5 to 6 at a time.
Let one side cook fully before turning. Fry until golden all over.
Remove and drain on a plate.
Place hot vada in a deep bowl. Pour hot rasam generously over the vada. Let soak for 3 to 5 minutes. Garnish with chopped coriander leaves and serve.
Notes
Soak urad dal overnight for the lightest, fluffiest vada.Always use chilled water when grinding the batter.Do not grind the batter smooth. A coarse texture gives the vada a better bite.Rest the rasam for at least 30 minutes after cooking.The flavour improves significantly.Fry vada on medium heat for even cooking all the way through.Adjust water in rasam depending on how thick or thin you like it.Soak vada in rasam just before serving.Do not leave them soaking for more than 15 to 20 minutes.