Ingredients

For dashi
3 (6-inch) pieces kombu (dried kelp)
1 qt water
1/2 cup tightly packed katsuo bushi (dried bonito flakes)
For shrimp cakes
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 lb) shrimp in shell without heads, peeled and deveined, finely chopped by hand or pulsed in a food processor
1/4 lb 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 qt vegetable oil

For wasabi vinaigrette
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

For mirin sauce
21/2 tablespoons mirin
21/2 tablespoons dark shoyu (Japanese soy sauce)
1 teaspoon sugar
1 teaspoon cornstarch mixed with 1 tablespoon cold water

For plating
6 oz mesclun (4 cups)
4 fresh shiso leaves, thinly sliced
3/4 cup tightly packed katsuo bushi
1 1/4 oz daikon sprouts, trimmed

Special equipment: cheesecloth; a deep-fat thermometer

Directions

SHRIMP CAKES WITH WASABI VINAIGRETTE:

Make dashi:
Wipe any sand or salt from kombu with a dampened cloth.
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.

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.

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.

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.

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.

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.