How to Make It
Melt butter in a large skillet over medium-high. Add shallot and garlic; and cook, stirring often, until softened, 2 minutes. Stir in chicken, and cook, stirring occasionally 2 minutes. Stir in alfredo sauce, Parmesan, salt, and pepper; cook, stirring often, until cheese is melted and sauce is heated through, about 5 minutes. Transfer mixture to a bowl, and cool completely, about 15 minutes; refrigerate until ready to use.
Preheat oven to 400°F. Roll out puff pastry to 1/8-inch thickness on a lightly floured surface. Cut each pastry sheet into 12 (4-inch) squares. Place 1 heaping tablespoon of the chicken mixture in the center of each square. Bush edges with some of the egg wash, and fold over to form a triangle, pressing edges to seal. Transfer to a baking sheet lined with parchment paper. Chill until firm, about 30 minutes.
Brush turnovers with egg wash. Bake in preheated oven until golden brown, about 20 minutes. Cool 5 minutes before serving.