Start with cooked, shredded chicken breast. If you don’t have pre-cooked chicken, poach it gently in simmering water until fully cooked, then shred with forks. Set aside. In a large skillet over medium heat, melt the butter.
Once the butter is melted, sprinkle in the flour, stirring constantly to form a smooth paste. Cook for about 2 minutes to remove the raw flour taste. This step is crucial to get a silky thick sauce.
Slowly whisk in the chicken broth and milk, making sure to break up any lumps. Add the salt, black pepper, garlic powder, and onion powder. Keep stirring until the mixture thickens and bubbles gently, about 5-7 minutes.
Stir in the shredded chicken and frozen mixed vegetables. Cook for another 2-3 minutes until the vegetables are heated through but still vibrant. Remove from heat and let cool slightly.
Preheat your oven to 425°F (220°C). Place one pie crust in the bottom of your pie dish, gently pressing it in. Pour the chicken and vegetable filling evenly into the crust. Cover with the second pie crust, trimming any excess dough, and crimp the edges to seal.
Brush the top crust with the beaten egg to create a golden, shiny finish. Use a sharp knife to cut a few slits in the top crust to allow steam to escape while baking.
Place the pie on a baking sheet to catch any drips and bake for 30-35 minutes, or until the crust is golden brown and the filling is bubbly. If the edges brown too quickly, cover them with foil.
Let the pot pie rest for 10-15 minutes before slicing. This resting time helps the filling set so it won’t spill out when you cut into it.