In a medium saucepan, melt the butter over medium heat. Add the chopped onion and diced carrots, cooking for 3-5 minutes until softened.

Sprinkle the flour over the vegetables and stir until coated. Cook for 1-2 minutes to eliminate the raw flour taste.

Gradually whisk in the chicken broth, ensuring no lumps form. Add the milk, garlic powder, thyme, salt, and pepper. Stir until the mixture thickens into a creamy sauce.

Stir in the cooked chicken and frozen peas. Remove from heat and let the filling cool slightly while preparing the crust.

Preheat your oven to 400°F.

Roll out the pie crust and place it into a 9-inch pie dish, letting the edges hang over slightly.

Pour the prepared chicken filling into the crust.

Fold the edges of the crust over the filling, or add a second crust on top for a double-crust pot pie. If using a top crust, crimp the edges to seal and cut a few small slits for steam to escape.

Brush the crust with beaten egg for a golden, shiny finish.

Place the pot pie on a baking sheet to catch any drips. Bake for 30-35 minutes, or until the crust is golden brown and the filling is bubbling.

Let cool for 5-10 minutes before serving.