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1
Soak the tamarind block in 750 ml of warm water for 10 minutes, using warm rather than cold water so the pulp loosens quickly and gives up its full yield of acid. Work it with the fingers until fully dissolved, then squeeze and press through a fine sieve, passing it through a second time if the liquid looks cloudy, so the finished broth stays clean and bright rather than muddy and bitter from stray fibre.
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2
Pour the strained tamarind water into a wide pan and add the cracked black pepper, cumin seeds, dried red chillies, crushed garlic, and rasam powder. Bring everything to a full rolling boil over medium-high heat, so the spices begin to open into the liquid before the tomatoes go in and are not simply stewing in a raw pool.
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3
Add the raw chopped tomatoes directly to the boiling tamarind water, then reduce the heat to a steady simmer and cook for approximately 10 minutes until the tomatoes have softened completely into the broth and the sharp, almost metallic edge of raw tamarind has cooked out. Season with salt. The broth must remain entirely thin and watery throughout — this is where the dish lives or dies — so if it shows any tendency to thicken, add a little hot water, because a rasam that reduces into body has crossed into sambar and is a different preparation entirely.
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4
Taste for sourness: rasam must be markedly, assertively sour, since the tamarind-acid character carries everything else and without it the pepper and spice have nothing to cut against. If the sourness is not immediately evident on the palate, the tamarind extract was too weak and this cannot be corrected by seasoning alone — adjust with a little more strained tamarind water. Lean over the pan and check that the pepper vapour is noticeable on the nose; if it is not, the broth needs another minute.
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5
Heat the oil or ghee in a small pan over high heat until shimmering, add the mustard seeds, and hold a lid above the pan so the seeds crackle and pop without scattering — the moment they do, add the curry leaves immediately, because a second's delay and the seeds will burn and turn bitter. The leaves will sputter violently; remove from the heat at once and pour the entire tadka into the rasam so the volatile fragrance of mustard and curry leaf hits the broth while it is still live. Serve immediately.