Cut a 1-inch-thick round from the center of the onion and separate it into rings (reserve the remaining onion for another use). Stack the rings directly on the griddle from largest to smallest so they form the shape of a volcano. Pour the brandy INSIDE the onion stack. Carefully, using a stick lighter, ignite the brandy and watch in awe. Once the flames subside, tumble the stack and dice the onions. Add the mushrooms, zucchini, yellow squash and carrot. Season with salt and pepper and saute until tender, about 10 minutes.
While the vegetables are cooking, add the hot dogs to the griddle. Cook, turning, until the hot dogs are nicely seared on all sides and the score marks have opened up, about 6 minutes. Brush on the teriyaki sauce and cook until the hot dogs are sticky and shiny!
Place the dogs in the buns, brush with more teriyaki sauce and top with the Pickled Hibachi Relish and a tight squiggle of Yum Yum Sauce. Sprinkle with toasted sesame seeds. Serve with the hibachi vegetables on the side.
Black Sesame Seed Hot Dog Buns:
Preheat the oven to 350 degrees F. Line a sheet pan with parchment paper.
Place the buns on the prepared sheet pan, brush with the melted butter and sprinkle the tops with sesame seeds. Bake for 4 minutes.
Pickled Hibachi Relish:
Put the zucchini, yellow squash and carrot in a medium heatproof bowl.
Bring the vinegar, salt, sugar and 3/4 cup water to a boil in a saucepan. Immediately pour into the bowl with the vegetables, then let cool on the counter until room temperature. Transfer to a resealable container and refrigerate for at least 1 hour. The vegetables will stay good for up to 2 weeks refrigerated.
Yum Yum Sauce:
Combine the mayonnaise, vinegar, tomato paste, butter, sugar, paprika, granulated garlic, hot sauce and onion powder in a medium bowl, whisk together and season to taste. Transfer to a squeeze bottle or resealable container and store in the refrigerator.