Cut the chicken into 1-inch pieces and season them with salt and pepper.

Dice the onion, carrots, and celery, mince the garlic, and slice the mushrooms.

Preheat your oven to 400°F (200°C).

Heat olive oil and 2 tablespoons of butter in a large pot, then add the diced onion, carrots, and celery and cook for 5-7 minutes until soft; add minced garlic and cook for 1 minute more.

Remove the cooked vegetables from the pot, add the remaining 2 tablespoons of butter, then add the sliced mushrooms and cook until brown and tender, about 5-8 minutes.

Add the seasoned chicken pieces to the pot and cook until lightly browned and mostly cooked through, about 5-7 minutes.

Sprinkle flour over the chicken and vegetables, stir well, and cook for 1-2 minutes to create a roux.

Slowly pour in chicken broth, stirring constantly until the mixture simmers and thickens.

Reduce heat to low, stir in heavy cream, cooked vegetables, mushrooms, peas, fresh thyme, parsley, salt, and pepper, cooking for 2-3 minutes until heated through; remove the filling from heat and let it cool slightly.

Unroll one pie crust and gently place it into a 9-inch pie dish, pressing it along the bottom and sides.

Pour the slightly cooled chicken and mushroom filling into the prepared pie crust.

Unroll the second pie crust and place it over the filling.

Trim excess crust, crimp the edges to seal, and cut a few small slits in the top crust for steam to escape.

Whisk the egg with 1 tablespoon of water in a small bowl and brush this egg wash over the top crust.

Bake for 35-45 minutes until the crust is golden brown and the filling is bubbly, covering the edges with aluminum foil if they brown too quickly.