Preheat your oven to 375°F (190°C).

In a large skillet, heat the olive oil over medium heat. Add the chopped onion and cook until softened, about 3-4 minutes. Add the minced garlic and cook for an additional 1 minute.

Add the diced carrots and celery to the skillet and cook until slightly softened, about 5 minutes.

Stir in the cooked chicken and frozen peas, and cook for another 2-3 minutes.

Sprinkle the flour over the chicken and vegetable mixture, and stir well to combine. Cook for 1-2 minutes to cook off the raw flour taste.

Gradually pour in the chicken broth and milk or cream, stirring constantly to prevent lumps from forming. Bring the mixture to a simmer and cook until thickened, about 5-7 minutes. Season with salt and pepper to taste.

Transfer the chicken mixture to a 9-inch pie dish or baking dish.

Roll out the pastry dough to fit over the top of the pie dish. Place the pastry over the filling, and trim any excess dough. Crimp the edges to seal, and cut a few slits in the top to allow steam to escape.

Place the pie dish on a baking sheet (to catch any drips) and bake in the preheated oven for 30-35 minutes, or until the crust is golden brown and the filling is bubbling.

Allow the Chicken Pot Pie to cool for a few minutes before serving. Enjoy the comforting flavors of this classic dish!