Preheat oven to 375°F. Line a 9 or 10-inch pie dish with one of the packaged pie crusts. Set aside. The other crust will be saved for the top.
Melt the butter in a large skillet over medium-high heat. Add the onion, celery, and carrots. Cook until vegetables are tender, about 5 minutes.
Add the garlic and cook for 1 minute. Add the cooked shredded turkey. Stir all the ingredients together and cook for an additional minute. You can add a splash of chicken broth if the mixture seems a little dry.
Stir in the frozen peas. Remove from heat and prepare the sauce.
In a large saucepan, melt the butter over medium-high heat. Gradually add the flour and stir into a paste.
Add the chicken broth and whisk together until the sauce starts to thicken. Add the parsley, thyme, nutmeg, salt, and pepper. Stir until all the ingredients are incorporated.
Stir in the heavy cream. Cook over medium heat, and stir constantly until the sauce thickens.
Pour the sauce over the vegetable/turkey mixture. Stir to combine.
Fill the pie crust in the prepared pan. Top with the second pie crust and form pie edges. Cut and X in the middle of the crust with a knife.
Bake for 1 hour or until fully baked. Remove from oven and let the pie sit for 10 minutes before serving.