Preheat oven to 425°F with rack in lower third position. On a lightly floured surface, roll puff pastry into an 11-inch square, then trim into an 11-inch circle. Cut 4 (1-inch) slits around the center of pastry, spacing each 1-inch apart. Place on a large plate or small baking sheet, chill in the freezer while you build the filling.

Whisk together mirin, chicken broth, soy sauce, and cornstarch in medium bowl until combined. Set aside.

Heat oil on a 10-inch cast-iron or medium ovenproof skillet over medium-high. Add mushrooms and cook, stirring occasionally, until lightly browned, about 10 minutes. Transfer to a small bowl.

Without wiping skillet clean, add pork; cook over medium-high, stirring often to break meat into crumbles, until no longer pink, about 5 minutes. Add cabbage; cook, stirring often until wilted, about 2 minutes. Add ginger, garlic, crushed red pepper, and white pepper; cook, stirring often, until fragrant, about 30 seconds. Re-whisk mirin mixture, then pour it into pork mixture. Bring to a simmer over medium-high and cook, stirring constantly, until sauce thickens slightly and flavors meld, about 2 minutes. Remove from heat; stir in scallions and reserved mushrooms until well combined.

Whisk together egg and water in a small bowl until thoroughly combined. Brush pastry evenly with egg wash. Sprinkle with sesame seeds. Place pastry over hot pork mixture, letting ends extend over sides of skillet.

Bake the potpie until top is browned and filling is bubbly, 20 to 25 minutes, rotating skillet front to back halfway through. Remove from oven and let stand 10 minutes before serving.