In a Dutch oven or large pot, melt 6 Tbsp butter over medium heat. Add the diced onions and sliced carrots, sautéing for about 8 minutes, until the vegetables are soft and fragrant.

Next, add the sliced mushrooms and minced garlic, cooking for an additional 5 minutes until the mushrooms are tender and release their juices.

Sprinkle the flour over the vegetable mixture, stirring constantly for 2 minutes to cook the flour. Gradually pour in the chicken stock and heavy cream, bringing the mixture to a gentle simmer.

Cook for 1 minute, or until the sauce thickens to a gravy-like consistency. Season the mixture with 2 tsp salt and 1/4 tsp black pepper, adjusting to taste.

Stir in the shredded chicken, frozen peas, and 1/4 cup parsley until fully combined. Remove from heat and allow the filling to cool slightly while preparing the crusts.

Roll out one chilled pie crust into a circle about 12 inches in diameter. Carefully transfer it into a deep 9-inch pie dish, ensuring it covers the edges.

Spoon the chicken filling into the crust, spreading it evenly.

Roll the second disk of pie crust into a 10-inch circle and place it over the filling. Tuck the excess dough underneath the bottom crust and crimp the edges together to seal the pie.

Using a sharp paring knife, cut 5 small slits in the top crust to allow steam to escape. Brush the top of the crust with the beaten egg and lightly sprinkle with coarse salt and pepper.

Bake in a preheated oven at 425°F for 30-35 minutes, until the crust is golden brown. If the edges begin to brown too quickly, cover them with a pie shield or homemade foil shield.

Once baked, allow the pie to rest for 15 minutes before slicing to let the filling set up.