1. Preheat the oven to 400°F (200°C). Lightly grease a 9-inch pie dish.
2. Melt the butter in a large skillet over medium heat. Add the onion, carrots, and celery and cook for 5–7 minutes, until softened. Add the garlic and cook for another minute.
3. Sprinkle the flour over the vegetables and stir for 1–2 minutes. Gradually whisk in the chicken broth and milk until smooth.
4. Bring the mixture to a gentle simmer and cook for 4–5 minutes, until the sauce thickens. Stir in the shredded chicken, frozen peas, thyme, parsley, black pepper, and salt.
5. Place one pie crust into the prepared pie dish. Pour the chicken filling evenly into the crust.
6. Cover with the second pie crust. Pinch the edges to seal, then cut a few small slits in the top to allow steam to escape.
7. Whisk the egg with 1 tbsp water and brush it over the top crust.
8. Bake for 35–45 minutes, or until the crust is golden brown and the filling is bubbling.
9. Let the pot pie rest for 10–15 minutes before slicing. Serve warm and enjoy this classic comfort-food favorite! 
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