In a 10-inch cast-iron skillet, melt butter over medium heat. Add onion, celery, carrot; cook until softened, 8 to 10 minutes. Add garlic; cook for 1 minute. Sprinkle flour over vegetables; cook, stirring constantly, for 1 minute. Gradually stir in broth and cream. Cook, stirring constantly, until mixture begins to thicken, 10 to 15 minutes. Remove from heat. Stir in turkey, peas, salt, thyme, parsley, and pepper.
Make Homemade Pie Dough
In the work bowl of a food processor, pulse together flour, sugar, and salt. Add cold butter, and pulse until mixture is crumbly and butter is pea-size. Add 5 to 6 tablespoons ice water, 1 tablespoon at a time, just until dough comes together.
Shape dough into a disk. Wrap tightly in plastic wrap and refrigerate for at least 30 minutes. Dough may be refrigerated for up to 3 days or frozen for up to 2 months.
Tip: Pie dough can be made up to 1 week ahead and stored in the refrigerator until ready to use. It can be stored in the freezer for up to 2 months.
On a lightly floured surface, roll Pie Dough to 14 inches and about ⅛-inch thickness. Place over hot turkey mixture, crimping as desired. Brush top of dough with egg. Cut 4 small slits in center of dough to release steam. Place skillet on a large, rimmed baking sheet.
Bake turkey pot pie for 15 minutes. Reduce oven temperature to 375°F. Bake until crust is puffed and golden brown and filling is bubbly, 40 to 45 minutes more, covering edges with foil to prevent excess browning, if necessary. Let cool for 15 minutes before serving.
Tip: For a quicker alternative using premade pie dough: Divide pie filling recipe in half to fill 1 (9-inch) pie plate, and cover with 1 premade pie crust; or prepare filling as directed to fill 2 (9-inch) pie plates, and cover each with 1 premade pie crust. If you make two pies but only need one, bake both and freeze one of the pies. Just make sure the pie is completely cool before wrapping securely with plastic wrap and placing in the freezer.
