01 - Preheat the oven to 400°F.
02 - Bring salted water to a boil in a medium saucepan. Add carrots, potatoes, and celery. Cook for 6–8 minutes until tender, then drain and set aside.
03 - Melt butter in a large skillet over medium heat. Add onions and sauté for 3–4 minutes until translucent.
04 - Stir the flour into the skillet and cook for 1–2 minutes, stirring constantly, to form a roux.
05 - Gradually whisk in the broth, followed by the milk, until smooth. Bring to a simmer and cook for 3–4 minutes until thickened.
06 - Add thyme, sage, salt, and pepper. Stir in the turkey, cooked vegetables, and peas. Simmer for 2–3 minutes.
07 - Transfer the filling to a 9-inch deep-dish pie plate or baking dish.
08 - Roll the puff pastry to fit the dish. Place over the filling, trimming excess edges. Press gently to seal and cut slits in the top to vent.
09 - Brush the pastry with the beaten egg.
10 - Bake for 30–35 minutes, or until the crust is golden and the filling is bubbling.
11 - Let the pot pie stand for 10 minutes before serving.