- Preheat your oven to 375°F. 
- Melt 1/2 cup butter in a large skillet over medium heat. 
- Add the carrots, potatoes, onions, and celery, cooking them until softened. 
- Add the flour to the skillet, stirring it in with the softened vegetables to create a thick paste. 
- Slowly whisk in the chicken broth and milk, letting the mixture simmer until it thickens. 
- Stir in the diced chicken and frozen peas. 
- Flavor everything with salt and pepper to your liking. 
- Pour the filling into a pie plate lined with the pie crust. 
- Make sure to spread it evenly across the bottom. 
- Cover the filling with another layer of pie crust. 
- Place the pie in the preheated oven, baking it until the crust turns golden brown, approximately 35-45 minutes. 
- Let the pie rest for 10 minutes before serving.