Yakisoba Pan

Start with the tangzhong by placing bread flour and milk in a saucepan. Heat over medium-high heat and whisk until it comes together, about 1 minute. Set aside and allow to cool down.
Combine the yeast and milk and let it rest for 5 minutes, allowing the yeast to become active.
Combine the bread flour, salt, and sugar in a large bowl of a stand mixer. Add the tangzhong, milk, and egg to the bowl and mix until it just comes together.
While the dough begins to knead, add the butter one tablespoon at a time. Knead the dough for 5 minutes. If the dough is too sticky, add 1 tablespoon of flour at a time. If it is too dry, add one tablespoon of milk at a time.
Transfer to an oiled bowl, cover, and let rest for 1 hour or until it has doubled in size. Once doubled, punch down and knead. Prepare a baking sheet by placing parchment paper down.
Divide the dough into 6 equal portions. Shape into round balls, roll into cylinders, and place on the baking sheet. Cover with plastic wrap and let rest for 30 – 60 minutes, or until doubled in size.
Preheat an oven to 375°F. In a small bowl, whisk an egg and 2 tablespoons of milk. Remove the plastic wrap from the baking sheet and brush each of the buns with egg wash. Place in the oven and bake for 15 to 20 minutes or until golden brown.

Heat a pan over medium-high heat with one tablespoon of canola oil. Add the onion, carrots, and mushrooms. Cook until the vegetables have softened, about 7 minutes. Add the napa cabbage and scallions. Cook until the cabbage has wilted.
Place the yakisoba noodles in a colander and run under hot water to seperate the noodles. Add the noodles to the pan and mix with the vegetables.
Add the yakisoba sauce and toss until completely coated. Turn off the heat and set aside until you are ready to make the sandwiches.

To prepare a sandwich, cut open the brioche bun on the top. Spread the inside of the bun with the butter. Add the mayo. Top with the yakisoba. Finally, top with a portion of anori and beni shoga.