In a saucepan over medium heat, melt the butter and stir in flour. Cook for one minute while stirring constantly.
Gradually whisk in the chicken broth and milk, and then add salt and pepper. Cook and stir until the mixture thickens and begins to bubble.
Mix in the cooked chicken and thawed peas and carrots. Remove from heat.
Place one crust in a pie pan, fill with the chicken mixture, and cover with the second crust. Seal and flute the edges, and cut several slits in the top to allow steam to escape.
Bake in the preheated oven for 30 to 35 minutes, or until the crust is golden brown. Let it cool for 10 minutes before serving.