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1
Soak the dried shiitake in 500 ml cold water for a minimum of four hours. Lift the shiitake clear and reserve them. Strain the soaking liquid carefully through a fine sieve or muslin to remove grit; this liquid is the flavour foundation of the nishime. Combine it with an equal or lesser volume of dashi to make the total cooking liquid. Score the konnyaku in a crosshatch pattern on both sides, then parboil in unsalted water for 3 minutes; drain and set aside. Peel and salt the satoimo, massage to draw out the mucilaginous coating, then rinse under cold water. Hold sliced gobō and renkon in cold water until required.
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2
Pour the combined dashi and shiitake soaking liquid into a wide, heavy pot. Add the soy sauce, mirin, and sugar; stir briefly. Bring to a gentle simmer over medium heat. Add the gobō, renkon, satoimo, takenoko, konnyaku, kombu, and reserved shiitake simultaneously — these are the dense, long-cooking elements. Partially cover the pot with a dropped lid (otoshibuta) or a circle of baking parchment pressed directly onto the vegetables. Simmer over medium-low heat for 30 minutes; the liquid should bubble gently at the edges and the vegetables should begin to take on colour from the seasoning.
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3
After 30 minutes, add the carrot pieces to the pot. Continue to simmer, partially covered, for a further 15 minutes. Test the gobō and renkon with a skewer: they should yield with slight resistance, neither chalky at the centre nor collapsing at the edges.
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4
This is where the nishime lives or dies. Remove the lid entirely. Raise the heat to medium so the liquid bubbles actively. Cook uncovered, moving the vegetables occasionally with a wide spoon, for a final 3–5 minutes. The liquid must reduce to a tablespoon's worth or less coating the base of the pot. As it does, it caramelises around the vegetables, and each piece takes on a lacquered, gleaming surface — teri wo tsukeru. The moment the vegetables gleam and the residual liquid is a thick, syrupy coating rather than a broth, the reduction is complete. Do not walk away: the transition from reduction to scorching is rapid.
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5
Remove the pot from the heat. Add the blanched snap peas or snow peas, folding them gently through the vegetables off the heat so they warm without losing colour. Taste a piece of satoimo or carrot: the seasoning should be deep and fully penetrated, sweet-savoury, with the dried shiitake providing a sustained bass note of umami. If the flavour is still surface-only, return to a very low heat for a further 5 minutes covered.
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6
Transfer the nishime to a lacquer box or serving dish, arranging pieces by colour where presentation demands it. The dish is complete as-is, but improves markedly if left overnight and reheated gently the following day, as the flavour continues to penetrate the interior of each vegetable.