How to Make It
Preheat oven to 350°F. Toss hazelnuts with 1 teaspoon water, oil, pepper, sugar, and salt in a small bowl until well coated. Spread in a single layer on a rimmed baking sheet. Bake in preheated oven, stirring occasionally, until toasted, 10 to 14 minutes. Remove from oven, and let cool completely, about 30 minutes.
Whisk together ketchup, soy sauce, and Worcestershire sauce in a small bowl until well combined.
Whisk together mayonnaise, yuzu kosho, and lemon juice in a small bowl until well combined. Refrigerate until ready to use.
Using a knife, shave off about 1/4 inch from top of florets of cauliflower head to create 2 tablespoons cauliflower crumbles; reserve crumbles for garnish. Quarter remaining cauliflower head, cutting through core. Using a mandoline, thinly slice some of the cauliflower quarters into about 1/8-inch-thick slices to equal about 4 cups. (Slices will be irregular in shape and vary in size.) Set slices aside. Transfer about 2 cups of florets to a small saucepan (reserve remaining cauliflower for another use). Add 3/4 cup water to saucepan. Bring to a boil over high. Reduce heat to medium-low; cover and simmer until cauliflower is tender, about 10 minutes. Drain well, and cool 15 minutes.
Transfer cooked cauliflower florets to a food processor, and process until smooth, about 30 seconds, stopping to scrape down sides as needed. Transfer 1/2 cup cauliflower puree to a large bowl, reserving remaining puree for another use. Whisk in eggs, potato starch, ginger, salt, pepper, and 1/4 cup scallions. Add cauliflower slices, and stir gently until evenly coated in potato starch mixture.
Heat 2 tablespoons oil in a 10-inch cast-iron skillet over medium until shimmering. Add batter, and press into an even layer covering bottom of skillet. Cook until bottom is golden brown, 6 to 9 minutes. Carefully transfer okonomiyaki to a baking sheet. Add remaining 2 tablespoons oil to skillet. Return okonomiyaki, browned side up, to skillet. Cook until bottom and sides are golden brown, 6 to 9 minutes. Transfer okonomiyaki to a serving plate.
Drizzle okonomiyaki with desired amount of bulldog sauce and yuzu kosho mayo. Sprinkle with roasted hazelnuts, remaining 1/4 cup scallions, and reserved shaved cauliflower crumbles. Cut okonomiyaki into slices, and serve immediately.
Kewpie mayonnaise and yuzu kosho can be found at Asian markets or online at amazon.com. To drizzle sauce and mayo, use a small squeeze bottle, or use a ziplock plastic bag with a small hole cut in one corner.