Heat olive oil in a large skillet over medium heat. Add onion, garlic, celery, and carrots. Cook, stirring occasionally, until vegetables are soft, about 5 minutes.
Stir in thyme, turkey, and flour. Cook for 1 minute, stirring constantly.
Add chicken broth, cream, salt, pepper, and nutmeg. Bring to a simmer and cook for 3 minutes, stirring occasionally.
Spoon mixture into a 9-inch pie dish. Place pastry crust over the top and trim any excess. Crimp edges of crust together.
Cut several slits in the top of the crust to allow steam to escape.
Bake for 30 minutes, or until crust is golden brown and filling is bubbling.
Interesting Facts
This dish is a great way to use up leftover turkey.
The addition of cream adds a richness to this dish.
You can substitute the pastry crust with biscuit dough for a more rustic flavor.