Ingredients

• 3 (6-inch) pieces kombu (dried kelp)
• 1 quart water
• 1/2 cup tightly packed katsuo bushi (dried bonito flakes)
• 2 tablespoons finely diced carrot
• 1/4 cup finely chopped onion
• 1/2 cup finely chopped fresh shiitake caps (2 large)
• 8 medium (31 to 35 per pound) shrimp in shell without heads, peeled and deveined, finely chopped by hand or pulsed in a food processor
• 1/4 pound skinless halibut, snapper, or cod fillet, finely chopped by hand or pulsed in a food processor
• 1 large egg yolk, lightly beaten
• 1/2 teaspoon fine sea salt
• 1 teaspoon light shoyu (Japanese soy sauce)
• 2 teaspoons sugar
• 1 quart vegetable oil
• 1 tablespoon prepared wasabi paste
• 1 tablespoon mayonnaise
• 1 tablespoon mirin (Japanese sweet rice wine)
• 1 tablespoon rice vinegar (not seasoned)
• White pepper to taste
• 2 1/2 tablespoons mirin
• 2 1/2 tablespoons dark shoyu (Japanese soy sauce)
• 1 teaspoon sugar
• 1 teaspoon cornstarch mixed with 1 tablespoon cold water
• 6 ounces mesclun (4 cups)
• 4 fresh shiso leaves, thinly sliced
• 3/4 cup tightly packed katsuo bushi (dried bonito flakes)
• 1 1/4 ounces daikon sprouts, trimmed
• Special equipment: cheesecloth; a deep-fat thermometer

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Instructions

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