Preheat the oven to 425 degrees Fahrenheit. Line a deep dish pie plate with one of the pie crusts. Set aside.
1 box refrigerated pie crusts
Melt the butter in a large skillet. Add the onion and garlic and season with salt and pepper. Cook for about 4 minutes, or until the onion is soft.
4 tablespoons unsalted butter, 1 small yellow onion, 2 cloves garlic, 1 teaspoon kosher salt, 1/2 teaspoon black pepper
Whisk in the flour. Then slowly whisk in the chicken broth, scraping up any browned bits. Whisk in the milk and thyme, and then bring to a simmer.
1/4 cup all purpose flour, 1 1/2 cups chicken broth, 1 cup milk, 1/2 teaspoon dried thyme
Stir in the chicken and vegetables so both are well coated with the gravy.
2 1/2 cups cooked shredded chicken, 2 cups frozen mixed vegetables
Pour the mixture into the prepared pie crust. Top with the second pie crust, and fold any extra pie crust over, tucking it under the first pie crust. Using two fingers on one hand and one finger on your other hand, work your way around the edge of the pie crust, fluting the pie crust (see photo in post). Cut three small slits in the top of the pie crust.
1 box refrigerated pie crusts
Bake for 15 minutes. Then, using a pie shield or aluminum foil, cover the edges (and/or the top) of the pie crust so they don't brown too quickly. Return to the oven and bake for 15 to 20 more minutes. Let the pie stand for 15 minutes before slicing and serving.