This kind of South Indian soup is called a rasam, which traditionally involves tamarind juice as base in addition to tomato, chili pepper, Pepper, Cumin and other spices as seasonings. Steamed lentils are often added, along with vegetables.
5 Tbsp picked-over split skinned toovar dal (a variety of pigeon pea, usually described as as yellow lentils)
4 Cups water
1-1/2 Tbsp ghee
1-1/2 tsp Black Mustard Seeds
1 fresh hot red chile such as serrano chile or Thai chile, halved lengthwise
1-1/2 pounds plum tomatoes, seeded and chopped
2 Tbsp finely chopped peeled fresh ginger
1 tsp Ground Coriander
1 tsp Tamarind
3/4 tsp Turmeric
1/2 tsp Ground Cumin
3 fresh hot green chiles such as serrano or Thai, halved lengthwise
fresh cilantro sprigs
Wash dal in several changes of water until water runs clear and drain well in a sieve. Cook dal at a bare simmer in 1-1/2 cups water in a 3-quart saucepan until most of water is evaporated and dal has consistency of a paste, 40 to 45 minutes, stirring frequently during last 15 minutes to prevent scorching.
Heat ghee in a 6-quart heavy saucepan over moderately high heat until hot but not smoking, then cook mustard seeds and red chiles, stirring, until seeds begin to pop. Add 1-1/2 Cups water and remaining ingredients (except the dal paste). Bring to a boil and simmer, stirring occasionally, until tomatoes are softened, 6 to 8 minutes.
Add dal paste and remaining cup water, stirring to incorporate. Bring rasam to a boil, stirring occasionally, and season with salt.