Preheat oven to 375°F (190°C).
Melt butter in a large skillet over medium heat.
Add onion and garlic and sauté until fragrant.
Stir in carrots and potatoes and cook for about 5 minutes.
Sprinkle flour over the vegetables and stir well.
Slowly add chicken broth while stirring to form a thick sauce.
Add heavy cream, shredded chicken, peas, thyme, salt, and black pepper.
Simmer the filling for about 5 minutes until thickened.
Pour the mixture into a baking dish and cover with pie crust.
Cut small slits in the crust for steam to escape.
Bake for 35–40 minutes until the crust is golden brown.