Preheat the oven to 425°F (220°C).
In a large dutch oven, melt 6 Tbsp of butter over medium heat. Add the chopped onions and carrots and sauté for 8 minutes until softened.
Stir in the mushrooms and garlic, cooking for an additional 5 minutes until the mushrooms are tender.
Sprinkle the flour over the mixture and cook for 2 minutes, stirring constantly.
Gradually add the chicken stock and heavy cream, stirring continuously until a thick gravy forms, about 1 minute.
Season with 2 tsp of sea salt and 1/4 tsp black pepper, or to taste.
Remove from heat and add the shredded cooked chicken, frozen peas, and parsley. Stir until combined. Let the mixture cool slightly.
Roll out one pie crust to a 12-inch diameter and fit it into a 9-inch pie dish. Spoon the chicken mixture into the pie crust.
Roll out the second pie crust to a 10-inch diameter and place it over the filling. Trim and crimp the edges to seal. Cut 5 small slits in the top crust to vent steam.
Brush the top of the pie with the beaten egg, and sprinkle lightly with coarse salt and pepper.
Bake for 30-35 minutes or until the top is golden brown. If the edges brown too quickly, cover them with a pie shield.
Remove the pie from the oven and let it rest for 15 minutes before slicing.