Make sure there is an oven rack on the bottom rack of the oven. Preheat oven to 400 degrees F.
Add the butter to a large skillet over medium heat. Once the butter is melted, add the chicken, carrots, celery, onion, salt, garlic powder, thyme leaves, and pepper. Cook for 8-10 minutes, until the chicken is cooked through, stirring often.
Add the flour. Stir well, until no dry flour remains. Slowly stir in the cream, then the chicken broth. Cook until bubbling and thick, stirring often, 3-4 minutes.
Remove from the heat. Stir in the peas and flat leaf parsley. Let this cool for 15-30 minutes before filling the pie.*
Fit one pie crust into a 9-inch pie plate. Spoon the cooled filling into the pie crust. Top with the second pie crust. Seal the edges of the pie crust together. Cut 3-4 slits in the top crust to allow steam to escape.
Place the filled pie plate on a baking sheet. Bake for 30 minutes on the bottom rack of the oven.
Cool for 15-30 minutes before slicing and serving.**