In a large skillet or saucepan, melt butter over medium heat. Stir in flour and cook for 1-2 minutes to form a roux.
Gradually whisk in chicken broth and milk until smooth. Cook, stirring constantly, until the mixture thickens, about 5 minutes.
Stir in cooked chicken, frozen vegetables, salt, pepper, thyme, and garlic powder. Remove from heat and let cool slightly.
Pour the filling into a 9-inch pie dish. Place the unbaked pie crust over the top, crimping the edges to seal. Cut a few slits in the center to allow steam to escape.
Optional: Beat the egg and brush it over the crust for a golden finish.
Bake for 40-45 minutes, or until the crust is golden brown and the filling is bubbling.
Let cool for 10 minutes before serving.
Notes
Serve warm with a side salad for a complete meal. Leftovers can be stored in the refrigerator for up to 3 days.