01 - Preheat your oven to 400°F.
02 - In a large skillet or Dutch oven, melt butter over medium heat. Add onions, carrots, celery, and potatoes (if using). Sauté for 5–7 minutes until softened. Add garlic and sauté 1 minute more.
03 - Stir in flour and cook for 2 minutes, stirring constantly, to form a roux.
04 - Gradually whisk in the broth and milk, ensuring no lumps remain. Bring to a simmer and cook until thickened, about 3–4 minutes.
05 - Stir in cooked turkey, peas, thyme, salt, and pepper. Taste and adjust seasoning. Remove from heat.
06 - Transfer the filling into a 9-inch pie dish or similarly sized baking dish.
07 - Roll out the puff pastry to fit the top of your dish. Lay pastry over filling, trim excess, and crimp edges. Cut a few small slits in the pastry to allow steam to escape.
08 - Brush the top with beaten egg.
09 - Bake for 25–30 minutes, or until the pastry is golden and crisp and the filling is bubbling.
10 - Let rest for 10 minutes before serving.