In a small skillet, heat butter and add the celery, carrots, onions, and garlic.
Over medium heat, allow the veggies cook while stirring constantly for about 5 minutes.
After veggies are fork-tender, add your flour to the mixture, and coat all veggies. Then, whisk in the heavy cream, and broth to create a roux. Continue to whisk until there are no lumps.
Add chicken to the pot, and spices. Simmer for 5-10 minutes on low heat until thickened.
Heat oven to 425°F. and line a large pie plate with one pie crust-prick holes in the bottom using a fork; set aside.
Once mixture is ready, add it to the pie, and then cover the top of the pie, and crimp edges. Be sure to add a hole, and slit to allow the pie to vent.
Bake for 35 minutes or until the pie is a golden brown color.
Allow pie to rest for 15 minutes before slicing.