Preheat your oven to 425°F (218°C) and place the oven rack in the middle position. Set the 9-inch (23 cm) deep-dish pie plate on a rimmed baking sheet to catch any bubbling filling during baking. Allow approximately 10 to 15 minutes for the oven to heat fully while you begin preparing the filling.

Melt the 1/4 cup (57 g) unsalted butter in a large skillet over medium heat. Add the 1 cup (70 g) chopped mushrooms, 1/2 cup (80 g) diced onion, and 1/2 cup (65 g) diced carrots. Cook for about 7 minutes, stirring occasionally, until the onion looks translucent, the mushrooms have released most of their moisture, and the carrots begin to soften. The vegetables should look tender around the edges without becoming deeply browned.

Sprinkle the 1/3 cup (40 g) all-purpose flour, 1/2 teaspoon (3 g) kosher salt, and 1/4 teaspoon (0.5 g) black pepper over the vegetables. Stir continuously over medium heat for about 1 to 2 minutes, until the flour coats the vegetables evenly and no dry white patches remain. The mixture will look thick and slightly pasty, which is normal.

Slowly pour in the 2 cups (480 ml) chicken broth while whisking or stirring to prevent lumps. Add the 1/2 cup (120 ml) whole milk and continue stirring over medium heat for approximately 4 to 5 minutes, until the sauce gently bubbles and thickens. It should coat the back of a spoon and look smooth and creamy rather than watery.

Stir the 3 cups (420 g) cooked turkey, 1/2 cup (80 g) frozen corn, and 1 cup (145 g) frozen peas into the sauce. Cook over medium-low heat for about 2 minutes, stirring gently, until everything is evenly coated and heated through. The filling should be thick enough to mound slightly on a spoon. Transfer it to the prepared deep-dish pie plate and spread it evenly.

Unfold the 1 sheet (approximately 8.65 oz / 245 g) thawed puff pastry onto a clean work surface. If necessary, gently roll it just enough to cover the 9-inch (23 cm) pie plate with a little overhang. Keep the pastry cool and avoid stretching it. It should feel flexible but not sticky or greasy.

Place the puff pastry over the filled pie plate and gently press it against the rim. Trim any excess pastry hanging far below the edge, then make 4 small slits near the center with a sharp knife to allow steam to escape. The pastry should cover the filling without being pulled tight, and the vent openings should be clearly visible.

Place the pie, still on its rimmed baking sheet, into the preheated 425°F (218°C) oven. Bake for approximately 20 to 30 minutes, until the puff pastry has risen, the top is deep golden brown, and the filling bubbles around the edges or through the vents. Check the center of the filling with a food thermometer; it should reach 165°F (74°C). If the pastry is browning too quickly, loosely shield the top with aluminum foil.

Remove the turkey pot pie from the oven and let it rest for 10 minutes before serving. The filling will continue to settle and thicken slightly, making it easier to spoon onto plates. The crust should remain golden and crisp, while the filling underneath stays hot and creamy.