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1
Cook the dal in sufficient water until fully tender — it should press to a smooth paste between thumb and finger with no chalky centre, because underdone dal will remain gritty once the coconut paste is folded in and the dish will not come together. Drain and set aside. Cook the ash gourd cubes separately in lightly salted water until just tender but still holding their shape, keeping them apart from the dal so each component reaches its own doneness without one turning to mush waiting for the other; the pieces must not collapse. Drain thoroughly.
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2
Dry-roast the coriander seeds, dried red chillies, black pepper, and cumin seeds together in a heavy pan over medium heat, stirring continuously, until the spices deepen in colour and a sharp, toasted aroma rises — the moment you smell that shift from raw to roasted the heat has done its work, and a moment beyond it tips into bitterness. Remove from the heat immediately and allow to cool. Grind the roasted spices together with the fresh grated coconut, adding just enough water to bring the mixture to a smooth, cohesive paste that still carries the volatile fragrance of raw coconut underlying the roasted note.
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3
Combine the drained dal and ash gourd in a wide pan, add the coconut-spice paste, and fold gently to coat so the ash gourd holds its shape rather than breaking under a heavy hand. This is where the dish lives or dies: cook over medium heat for 5–8 minutes, stirring at intervals, until the raw coconut taste — distinct and unpleasant — has cooked fully away and the moisture has reduced until the mixture is thick and almost dry, each piece coated in masala with no standing liquid in the pan.
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4
Stir in the pinch of jaggery to round the edge of the spices without sweetening the dish outright, then adjust the salt. Remove from the heat.
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5
Heat the coconut oil in a small pan until shimmering, add the mustard seeds, and wait for them to splutter and pop — pouring them too early, before the seeds have fully crackled, leaves a flat, unfinished note in the finished dish. Add the curry leaves and dried red chillies; they will crackle and turn fragrant within seconds. Pour the tadka immediately over the kootu — the hiss of hot oil meeting the cooked mixture signals the finish.