In a large skillet, melt butter over medium heat. Add the onion and potatoes, and cook for 10 minutes, stirring frequently.
Stir in the flour. Cook, stirring constantly, for 2 minutes. While stirring, slowly pour in the broth and heavy cream. Add the poultry seasoning, salt, and pepper. Reduce the heat to low.
Stir in the frozen vegetables and turkey, and cook for 5 minutes. Pour the filling into a bowl to cool.
Preheat the oven to 425F. Beat the egg with 1 teaspoon of water.
On a lightly floured surface, roll one pie crust to a 12-inch circle. Transfer to a deep 9-inch pie plate. Pour in the cooled filling.
Roll out the remaining pie crust and place it on top of the filling. Trim the excess crust within 1 inch of the edge of the pie plate. Tuck the edges under and crimp as desired. Brush the pie crust with the beaten egg. Cut a few slits in the top of the crust to vent steam. Place it on a rimmed baking sheet.
Bake for 20 minutes.
Reduce the heat to 350F and continue baking until the crust is a deep golden brown and the filling is bubbling, about 30 minutes.
Let the pie cool for 10 to 15 minutes before serving. Sprinkle with flaked salt and pepper.