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 ½ 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 chile, stirring, until seeds begin to pop. Add 1‚ cups water and remaining ingredients (but not 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.
Note: Yield: 6 Servings, Makes: 5 cups