Step 1: Preheat your oven to 400°F (200°C).
Step 2: In a large skillet or Dutch oven, melt the butter over medium heat. Add the onion, carrots, and celery. Sauté for 8-10 minutes until the vegetables are softened.
Step 3: Stir in the minced garlic and cook for another minute until fragrant.
Step 4: Sprinkle the flour over the vegetables and stir constantly for 1-2 minutes to create a roux.
Step 5: Slowly whisk in the broth and heavy cream. Continue to stir until the mixture thickens and comes to a gentle simmer.
Step 6: Season with salt, pepper, thyme, and sage. Fold in the cooked wild turkey and frozen peas.
Step 7: Pour the turkey mixture into a 9-inch deep-dish pie plate or casserole dish.
Step 8: Roll out the puff pastry and place it over the filling. Trim the edges and cut 3-4 small slits in the center for steam.
Step 9: Brush the pastry with a beaten egg wash for a golden finish.
Step 10: Bake for 30-35 minutes, or until the crust is puffed and golden brown and the filling is bubbling.
Step 11: Allow the pie to rest for 10 minutes before serving to let the sauce set.