Melt butter in a skillet over medium heat. Add onions and cook for about 5 minutes until translucent and tender.
Stir in flour, salt, and pepper until the mixture starts to bubble.
Pour in chicken broth and milk. Bring to a boil and cook until mixture thickens up, about 3 minutes.
Take off the heat and mix in chicken and vegetables.
Lay a store-bought pie crust in a 9" pie plate. Place pie bird right in the middle. Pour the filling in.
Cut an X in the middle of the top crust if using the pie bird, or several slits if you're not. Lay the second crust on top so the pie bird pops through and seal the edges. Crimp the edges with a fork.
Bake for 15-20 minutes. Pull out of the oven and place a pie crust shield or aluminum foil over the edges of the crust to prevent it from burning. Pop back in the oven and bake for another 15-20 minutes. Let sit for 5-10 minutes before slicing and digging in.