Step 1In a saucepan, bring the water, soy sauce, mirin and kombu to a boil over medium heat. Boil for 30 to 45 seconds, then remove from heat and add the bonito flakes.
Step 2Let the broth steep for 3 to 5 minutes. Strain the broth through a fine mesh strainer, discarding the kombu and bonito flakes. Cool the broth, then refrigerate. It can be made up to a week ahead and kept refrigerated and tightly covered. Makes 3 cups.
Step 1In a saute pan, heat the olive oil and butter over medium-high heat. When the butter sizzles, add the mushrooms, season with salt and pepper and cook just until they soften, about 1 to 2 minutes. Remove from heat and cool. Refrigerate until ready to use.
Step 1Bring a large pot of lightly salted water to a boil over high heat. Add the soba noodles and cook until foam rises to the top, about 30 seconds. Reduce heat and simmer until noodles are tender but springy. Depending on the brand, this can take anywhere from 1 to 5 minutes; the only way to be sure is to taste.
Step 2When the noodles are done, pour them into a strainer and rinse under cold running water until the water runs clear. When the noodles are cool, drain them and divide them among 4 bowls; refrigerate.
Step 1Rinse the fish and pat it dry. Season it with salt and pepper and lightly dust it with flour.
Step 2Heat the olive oil and butter in a skillet over medium-high heat. When the butter sizzles, add the flounder pieces, being careful not to overcrowd the pan. Cook until they are crisp on both sides, about 4 to 6 minutes total cooking time. Remove them from the pan and lift the fillets from the bones. (If they don't lift easily, cook them a little more.)
Step 3Add about two-thirds cup chilled dashi broth to each of the 4 bowls of chilled soba noodles. Place the chilled mushrooms and hot fish on top of the noodles. Garnish with the shredded nori and kaiware sprouts. Artfully smear a little less than a teaspoon of wasabi along one side of the bowl. Serve immediately.