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