01 - Preheat the oven to 400°F.
02 - Melt butter in a large skillet or Dutch oven over medium heat. Add onions, carrots, celery, potatoes, and garlic, sautéing for 5-7 minutes until softened.
03 - Incorporate flour into the vegetables, stirring constantly and cooking for 1-2 minutes.
04 - Gradually whisk in the broth and milk, stirring until smooth. Bring to a simmer and cook for 5-7 minutes until the sauce thickens.
05 - Stir in salt, pepper, thyme, and sage. Add turkey and peas, cooking an additional 2 minutes to combine flavors.
06 - Transfer the mixture to a 9-inch deep-dish pie plate or similar baking dish.
07 - Unroll thawed puff pastry and place it over the filling, trimming excess dough. Press edges to seal and cut small slits to allow steam to escape.
08 - Brush the pastry surface with beaten egg to achieve a golden finish.
09 - Bake for 30-35 minutes until the pastry is golden and the filling bubbles.
10 - Allow to rest for 10 minutes before serving.