The soup is cold and the rice is hot, and that contrast is the point of the dish rather than an accident of the serving.
The name is old — it turns up in a Kamakura-period record, and monks are said to have carried the idea around the country. A horse mackerel or a sea bream is grilled without seasoning, the flesh is picked off it and the bones taken out carefully, and white sesame is ground in a mortar until it turns to paste. Fish and miso go in and are ground together with it. The paste is toasted briefly over the fire and then let down with dashi, thicker than a miso soup would ever be.
Sliced cucumber goes in, and crumbled tofu, and chopped shiso and myoga. You pour the whole cold thing over hot barley rice and eat it quickly. The account of its origin is simpler than the recipe: farm workers in the summer heat used to put raw miso onto barley rice and pour water over that. It is home cooking, so the method shifts from district to district within the prefecture. Nobody's version is the correct one.
It used to appear at the end of the evening when relatives gathered at the old house for the summer festival of the dead. Ending a hot night with something cold, rather than with something warming, is a piece of reasoning that belongs to a hot part of the country.
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