Preheat the oven to 425°F.
In a large skillet over medium heat, melt the butter. Add the chopped onion and celery, and sauté until softened, about 3-4 minutes.
Stir in the flour, garlic powder, thyme, salt, and pepper, and cook for another minute.
Gradually whisk in the chicken broth and milk, stirring constantly until the mixture thickens, about 3-5 minutes.
Add the cooked chicken, peas, carrots, and potatoes, and mix well. Remove from heat.
Unroll one pie crust and place it in a 9-inch pie dish. Pour the chicken mixture into the crust.
Unroll the second pie crust and place it over the filling. Trim and crimp the edges to seal. Cut a few slits in the top crust to allow steam to escape.
Bake in the preheated oven for 30-35 minutes, or until the crust is golden brown. If the edges brown too quickly, cover them with foil.
Let it cool for 10 minutes before serving.