Line an 18- x 13-inch rimmed baking sheet with parchment paper; set aside.

Cook hot sauce and butter in a small saucepan over medium, stirring occasionally, until butter melts, about 2 minutes. Pour into a medium-size heatproof bowl, and let cool slightly, about 10 minutes. Stir in turkey, celery, scallions, kosher salt, and pepper. Refrigerate, uncovered, until ready to use.

Stir together egg and 1 tablespoon water in a small bowl; set aside. Working quickly, roll out puff pastry to a 20- x 12-inch rectangle on a lightly floured work surface with short edge facing you; dust puff pastry with flour as needed to prevent sticking. Slice in half crosswise. Slice each half into 3 (10- x 4-inch) rectangles.

Spoon 1/3 cup turkey mixture onto bottom half of each rectangle, leaving a 3/4-inch border along bottom and sides. Top each with 2 tablespoons cheese. Working with 1 rectangle at a time, lightly brush bottom and side border of puff pastry with egg mixture. Fold top half of puff pastry over filling, and gently press edges together to seal. Crimp edges using a fork. Gently transfer hand pies to prepared baking sheet, spacing evenly apart. Brush hand pies with egg mixture. Cut 2 (3/4-inch) slits on top of each hand pie using a paring knife. Sprinkle hand pies with additional pepper to taste, and garnish with flaky sea salt. Freeze 30 minutes. Meanwhile, preheat oven to 425°F.

Remove hand pies from freezer, and bake in preheated oven until hand pies are slightly puffed and lightly browned on top, about 15 minutes. Reduce oven temperature to 375°F, and bake until pies are puffed, browned, and crisp, 20 to 25 minutes. Let stand 10 minutes.