01 - Preheat oven to 400°F.
02 - Melt butter in a large skillet over medium heat. Add onion, carrots, and celery. Sauté 5–7 minutes until softened. Add garlic and cook 1 minute more.
03 - Sprinkle flour over vegetables; stir and cook for 2 minutes to form a roux.
04 - Gradually whisk in chicken broth, milk, and cream. Bring to a simmer, stirring constantly, until mixture thickens, about 3–5 minutes.
05 - Stir in turkey, peas, salt, pepper, thyme, and sage. Simmer 2 minutes. Remove from heat.
06 - Spoon the filling into a 9-inch deep-dish pie plate or similar baking dish.
07 - Roll out the puff pastry to fit your dish. Place over filling, pressing edges to seal. Cut slits on top to vent steam.
08 - Brush pastry surface evenly with beaten egg.
09 - Bake 25–30 minutes, or until pastry is golden brown and filling is bubbling.
10 - Let rest 10 minutes before serving to allow filling to set.