For the Fuku patty: In a blender, mix the mirin, sake, soy sauce, sugar, sesame oil, yuzu, garlic, onion powder and pepper until smooth. Gently massage the marinade into the ground beef and let sit for at least 2 hours. Form the beef mixture into a disk and chill in the refrigerator.
For the wasabi mayo: Mix the soy sauce and wasabi powder to a thin consistency. Whisk the mixture into the mayonnaise.
For the teriyaki: Reduce the mirin and sake in a saucepan to three-quarters of the original volume. Add the soy sauce and sugar. Bring to a boil. Whisk together the cornstarch and 2 tablespoons water to make a slurry. Add the slurry to the pan and bring to a boil. Let cool before using.
For the crispy fried onions: Thinly slice the onion into 1/3-inch rings. Heat the canola oil in a deep fryer to 400 degrees F. Dredge the onions in flour and shake off the excess. Fry until golden brown, about 8 minutes. Drain on layered paper towels and season with salt.
For the Tamago burger: Heat the canola oil in a skillet over high heat. Place the Fuku patty in the pan and turn down the heat to medium. Cook for 2 to 2 1/2 minutes per side. Place the patty on the bottom half of a bun and top with the fried egg. Drizzle with 1/2 teaspoon teriyaki sauce and sprinkle with Tamago Furikake to taste (Furikake should stick to the egg). Top with crispy fried onions and drizzle with 1/2 to 1 teaspoon wasabi mayo.
For presentation, lean the bun top against the side of the assembled burger to showcase your hours of hard work.
This recipe was provided by a professional chef or restaurant and may have been scaled down from a bulk recipe. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.