Step 1: Preheat and Prepare. Preheat your oven to 425°F (220°C). Prepare your 9-inch pie plate by placing one of the pie crusts into the bottom, pressing it firmly against the bottom and sides.
Step 2: Sauté the Vegetables. In a large saucepan, melt the butter over medium heat. Add the chopped onions and sliced celery. Cook them for about 5 to 7 minutes, or until the vegetables are tender and the onions are translucent.
Step 3: Create the Roux and Season. Stir the flour, salt, black pepper, and celery seed into the sautéed vegetables. Cook for 1 minute while stirring constantly to remove the raw flour taste. This creates the base for your creamy sauce.
Step 4: Simmer the Sauce. Slowly whisk in the chicken broth and milk. Continue to cook and stir over medium-heat until the mixture bubbles and thickens. This usually takes about 5 to 8 minutes.
Step 5: Combine Filling Ingredients. Stir in the cooked chicken and the thawed peas and carrots. Remove the saucepan from the heat once everything is well combined and heated through.
Step 6: Assemble the Pie. Pour the chicken mixture into the prepared bottom pie crust. Cover with the second pie crust. Seal the edges by crimping them with your fingers or a fork. Cut several small slits in the top crust to allow steam to escape during baking.
Step 7: Bake to Golden Perfection. Place the pie in the preheated oven and bake for 30 to 35 minutes. The crust should be a beautiful golden brown and the filling should be bubbly. Let the pie stand for 5 to 10 minutes before cutting to allow the filling to set.