Preheat your oven to 400°F (200°C).
In a large skillet, sauté the onions, garlic, carrots, mushrooms, and peas in a bit of oil over medium heat until the vegetables are tender.
Add the butter to the skillet and let it melt. Sprinkle the flour over the vegetables and stir continuously to create a roux. Cook for 2-3 minutes to remove the raw flour taste.
Gradually pour in the heavy cream, milk, and chicken broth while stirring constantly to avoid lumps. Continue stirring until the mixture thickens.
Season the mixture with salt, pepper, and garlic powder. Add in the shredded chicken and mix well.
Roll out one sheet of puff pastry and line a pie dish with it. Trim any excess pastry hanging over the edges. Fill the pastry-lined dish with the chicken and vegetable mixture.
Roll out the second sheet of puff pastry and place it over the filling. Press the edges of the top and bottom pastry sheets together to seal the pie. Trim any excess.
Brush the top of the puff pastry with the beaten egg. This will give it a beautiful golden finish.
Place the pie in the preheated oven and bake for 25-30 minutes or until the pastry is golden brown and the filling is hot and bubbly.
