Preheat oven to 375°F and grease a 9x13-inch baking dish. On a lightly floured surface, overlap two pie crusts slightly and roll them together into a rectangle large enough to line the bottom and sides of the dish; fit the crust into the dish.
In a large saucepan over medium heat, whisk together cream of chicken soup, milk, chicken broth, and flour until smooth and thickened, about 5 minutes.
Stir in chicken, frozen vegetables, thyme, garlic powder, pepper, and salt until well combined.
Pour the chicken mixture over the bottom pie crust in the baking dish.
Overlap and roll the remaining two crusts into a rectangle large enough to cover the dish. Place it over the filling, crimp the edges to seal, and cut several slits in the top to vent.
Bake for 40-45 minutes until the crust is golden brown and the filling is bubbly.
Allow to cool for 10 minutes before serving.