medium green cabbage (about 1 pound)
medium carrots (about 6 ounces total)
medium scallions
water
large eggs
kosher salt
all-purpose flour
toasted sesame oil
ketchup
Worcestershire sauce
oyster sauce
mayonnaise
rice vinegar
Furikake
Katsuobushi (bonito flakes)
Prepare the following ingredients, adding each to the same large bowl as you complete it: Cut 1/2 medium cabbage in half and cut out the core. Very thinly slice the cabbage until you have about 4 packed cups. Peel 2 medium carrots and grate on the large holes of a box grater (1 1/2 cups). Thinly slice 4 medium scallions, then reserve 2 tablespoons of the dark green parts for garnish and add the remaining scallions to the cabbage mixture. Toss to combine.
Place 1/2 cup water and 1 tablespoon hondashi in a liquid measuring cup or medium bowl and whisk to combine. Add 2 large eggs and 1 1/2 teaspoons kosher salt, and whisk to combine. Pour over the cabbage mixture and toss to combine.
While stirring constantly, slowly sprinkle in 1 cup all-purpose flour and toss until all the flour is absorbed and the cabbage mixture is evenly coated. Set aside to rest for 5 minutes. Meanwhile, heat a medium nonstick skillet over medium heat.
Add 2 tablespoons toasted sesame oil to the pan and swirl the pan to coat. Using tongs, add the cabbage mixture to the pan and scrape in any residual batter, then spread into an even layer. Cover and cook until deep golden-brown on the bottom, 8 to 10 minutes (check by using a spatula to lift up and look under a section).
Shake the skillet to loosen the pancake. Uncover and slide the pancake onto a large plate browned-side down. Carefully invert the skillet over the plate. Using oven mitts, place one hand under the plate and the other hand on the bottom of the skillet, then flip both together in one motion to return the pancake to the skillet. Continue to cook over medium heat until the second side is deep golden-brown and the vegetables in the center are cooked through, 6 to 8 minutes more. Meanwhile, make the sauce and seasoned mayonnaise.
Place 1/3 cup ketchup, 1 tablespoon Worcestershire sauce, and 1 tablespoon oyster sauce in a small bowl and whisk to combine.
Place 1/3 cup mayonnaise and 1 tablespoon rice vinegar in a second small bowl and whisk to combine.
When the okonomiyaki is ready, slide it onto a serving plate. Dollop the sauce and seasoned mayonnaise over the top. Sprinkle generously with furikake and the reserved scallion greens. Cover the entire surface with a generous amount of katsuobushi. Cut into wedges and serve