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1
Wipe any sand or salt from kombu with a dampened cloth.
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2
Bring water and kombu almost to a boil in a 2-quart saucepan, then reduce heat and simmer, uncovered, 5 minutes.
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3
Add katsuo bushi and bring to a boil, then boil 30 seconds.
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4
Remove from heat and let stand 3 minutes, skimming any foam.
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5
Pour dashi through a cheesecloth-lined sieve into a bowl.
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6
Cook carrot, onion, and mushrooms in 1/4 cup dashi, uncovered, in a small heavy skillet over moderate heat, stirring frequently, until carrot and onion are softened, about 4 minutes.
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7
Cool slightly.
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8
Stir together shrimp, fish, vegetable mixture, yolk, sea salt, shoyu, and sugar in a bowl until combined well, then knead with your hands to form a paste.
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9
Chill, covered, until cold, about 1 hour.
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10
Whisk together wasabi paste and mayonnaise, then add mirin and rice vinegar in a slow stream, whisking until blended well.
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11
Season with white pepper.
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12
Bring mirin, shoyu, sugar, and 1/4 cup dashi to a simmer in a small saucepan.
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13
Stir cornstarch mixture, then whisk into mirin mixture and boil, whisking, 1 minute.
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14
Remove from heat and keep warm, covered.
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15
Heat oil in a deep 10-inch skillet over moderate heat until it registers 250F on thermometer.
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16
While oil is heating, form shrimp mixture into 4 (1/2-inch-thick) cakes.
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17
Fry cakes until light golden, about 2 minutes on each side, then transfer with a wide metal spatula to paper towels to drain.
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18
Transfer cakes with spatula to clean paper towels to drain again.
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19
Cut each cake into 1/2-inch-wide slices.
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20
Divide mesclun among 4 plates and sprinkle with shiso leaves.
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21
Arrange shrimp cake slices over salads and drizzle with vinaigrette and mirin sauce.
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22
Top each serving with 2 rounded tablespoons katsuo bushi, then with sprouts.
