To fry and mold the wontons: Heat about 4-inches of oil in a deep saucepan over medium-high heat until it reaches a temperature of 350 degrees F (the oil can be tested by carefully dripping a little water into it—if it immediately sizzles, it is hot enough). Brush the edge of a wonton wrapper with beaten egg, then mold the wrapper around a metal pastry tip or other heat resistant conical mold. Lower the wrapper and mold into the hot oil and fry, until golden brown. Remove the fried wonton from the oil, transfer to a plate lined with paper towels to drain and cool. Remove the mold and repeat, molding and frying all the ‘wonton cones’.

To make the dressing and salad: In a small bowl, combine the soy sauce, rice vinegar, wasabi, sugar, and mayonnaise. Gradually whisk in 2 tablespoons of peanut oil.

In a separate bowl, combine the cucumber, avocado, scallion, and shiso. Lightly dress the cucumber salad with the wasabi dressing.

To make tuna and tobiko tartar: Finely chop the tuna and set it aside. In a medium bowl, mix the mayonnaise, lemon juice and sour cream. Fold first the tobiko eggs, then the tuna into the mayonnaise mixture.

To assemble: Place each wonton in a paper or aluminum foil cone. Fill each about two-thirds with cucumber salad. Spoon tuna and tobiko tartar into the cones, sprinkle with furikaki and serve.