In a large pot, melt 3 tablespoons of unsalted butter over medium heat. Once melted, add 1 diced onion and 2 sliced carrots, sautéing until the onion is translucent, about 5 minutes. Then, stir in 8 ounces of sliced mushrooms and 2 minced garlic cloves, cooking for another 3-4 minutes until all vegetables are tender and aromatic.

Sprinkle 1/3 cup of all-purpose flour over the sautéed vegetables, stirring constantly for about 2 minutes.

Gradually pour in 2 cups of low-sodium chicken stock and 1 cup of heavy cream to the roux, stirring continuously until the mixture is thick and smooth.

Off the heat, stir in 2 cups of shredded cooked chicken and 1 cup of frozen peas. Add 1 tablespoon of chopped fresh parsley.

Roll out one disk of pie dough to fit your pie dish, about 12 inches in diameter. Spoon the filling into the crust, and cover with a second rolled-out crust.

Preheat your oven to 425°F (220°C). Brush the top crust with a beaten egg and bake for 30-35 minutes.

Once baked, remove from the oven and let it rest for 10-15 minutes before serving.