Special equipment: Small Mixing Bowl Large Mixing Bowl Food Processor Knife for slicing vegetables Cutting Board Basting Brush Measuring Spoons Measuring Cups Mixing Spoon Spatula Bread Knife
Mayonnaise: Stir water into the wasabi powder in a small bowl and let stand for 5 minutes. Stir in mayonnaise.
Burgers: Using your hands, gently mix turkey with scallions, soy sauce, mirin, sesame oil and 1 teaspoon of the salt in a large bowl. Divide turkey mixture into 6 equal portions, then into balls by gently tossing from hand to hand. Shape into 6 loosely packed 1-in. thick patties. Press the center of each patty so it is slightly thinner than the edges. Brush with oil and season the outside with salt and black pepper to taste.
Grill burgers, turning once, until cooked through, about 14 minutes total. Set burgers aside to rest while grilling the buns until lightly toasted. Season the avocado and tomato with salt to taste. Serve the burgers on the buns with the wasabi mayonnaise, avocado, tomato, sprouts and pickled ginger.