Preheat your oven to 375°F (190°C).
In a large skillet, melt the butter over medium heat.
Add the chopped onion and minced garlic to the skillet and sauté until the onion is translucent, about 3-4 minutes.
In a large mixing bowl, combine the cooked turkey, diced carrots, chopped green beans, cooked peas, sautéed onion and garlic, dried thyme, salt, and black pepper.
Pour the turkey gravy over the mixture and stir gently to combine all ingredients evenly.
Roll out one pie crust and fit it into a 9-inch pie dish, pressing gently to fit the shape.
Spread the turkey and vegetable mixture evenly into the pie crust.
Drop spoonfuls of mashed potatoes over the filling and gently spread to cover the filling completely.
Cover the pie with the second pie crust. Trim any excess dough and crimp the edges to seal.
Cut a few small slits in the top crust to allow steam to escape during baking.
Place the pie on a baking sheet and bake in the preheated oven for 35-40 minutes, or until the crust is golden brown and the filling is bubbly.
Remove the pie from the oven and let it cool for 10 minutes before serving.