In a saucepan, melt the butter over medium heat. Add the onions, carrots, and celery. Cook until tender.
Stir in the flour, salt, and pepper until well blended. Gradually stir in the chicken broth and milk. Cook, stirring constantly until thickened.
Add the shredded chicken and peas to the mixture. Remove from heat.
Place one pie crust in a pie dish. Pour the chicken mixture into the crust. Cover with the second pie crust. Seal the edges and cut away excess dough. Make several small slits in the top crust to allow steam to escape.
Bake in the preheated oven for 30-35 minutes, or until the crust is golden brown. Let cool for 10 minutes before serving.