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1
Place the rinsed azuki beans in a pot and cover generously with cold water. Bring to the boil, drain, and discard this first water. This preliminary boil removes harsh tannins. Cover again with fresh cold water — for zenzai, add the konbu now. Simmer over low heat, replenishing water as needed, until the beans are fully tender throughout and crush without resistance between the fingers. Do not add sugar at any point during this stage; osmotic toughening will prevent the beans from cooking through.
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2
Remove the konbu (zenzai). For zenzai: the cooking liquid is retained — do not discard it; its colour and flavour from the azuki's water-soluble pigments are part of the soup. For shiruko: pass the cooked beans and their liquid through a fine sieve or strainer, pressing firmly to extract all paste while discarding skins. Thin the resulting paste with water to a smooth, poured consistency in which no whole beans are visible. Both preparations should now read as a coherent liquid base.
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3
Add the sugar to the prepared base in stages — not all at once — stirring between additions and tasting. The bean's natural flavour must remain perceptible; the target is sweet but not overwhelming. This is the step on which the dish lives or dies: the proportion and staging of sugar determines whether the preparation expresses the azuki or merely masks it. Add the sake in the final minutes of cooking to remove the raw bean aroma and round the flavour.
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4
Add a small pinch of salt and stir through. Taste immediately: the sweetness should sharpen and the bean's earthiness become more legible. This is the Japanese 'salt in sweet' principle (shio de amasa wo hikitateru). Without it, the sweetness is one-dimensional. The soup is now complete.
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5
Toast the mochi pieces in a dry frying pan or under a broiler. The surface should blister and char in distinct spots; the interior remains soft and glutinous. The charred patches, detected by smell and sight before the mochi is placed, provide the bitter complexity that cuts through the sweet broth. Cold or room-temperature mochi must not be used — it becomes hard and unpleasant in the soup.
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6
Bring the soup to a full, vigorous heat — it is served hot, not warm; temperature is intrinsic to its identity as a winter preparation. Ladle into warmed bowls and place the toasted mochi directly in the soup at the moment of service. The mochi should soften partially in the hot liquid while retaining a slightly charred, crisp surface. Serve immediately, with a small plate of salt-pickled daikon or nozawana alongside if desired.