Preheat your oven to 400 degrees Fahrenheit. Lightly grease a 9-inch deep dish pie pan or casserole dish.

In a large skillet over medium heat, melt the butter. Add the diced onion and cook for 3-4 minutes until softened. Sprinkle in the flour and stir constantly for 1 minute to create a roux.

Gradually whisk in the chicken broth and milk, stirring constantly to prevent lumps. Add the thyme, salt, and pepper. Bring to a simmer and cook for 3-5 minutes until the sauce thickens.

Stir in the cooked chicken and mixed vegetables. Cook for 2-3 minutes until everything is heated through and well combined. Taste and adjust seasoning as needed.

Place one pie crust in the bottom of your prepared dish. Pour the chicken and vegetable mixture over the crust. Top with the second pie crust, crimping the edges to seal. Cut 4-5 small slits in the top to allow steam to escape.

Place the pie on a baking sheet to catch any drips. Bake for 30-35 minutes until the crust is golden brown and the filling is bubbling through the vents.

Remove from the oven and let rest for 10 minutes before slicing. This allows the filling to set slightly for easier serving. Enjoy warm.