Preheat your oven to 375°F (200°C).
Season the chicken with garlic powder, salt and pepper.
Heat the oil in a large skillet over medium-high heat. Cook the chicken breasts for 4-5 minutes on each side or until fully cooked and an instant read thermometer inserted into the center reads 165°F. Shred the chicken and set aside. (You should have about 1 1/2 cup shredded chicken breast.)
In a large skillet or Dutch oven over medium heat, melt 2 tablespoons of butter. Add the potatoes, mushrooms, carrots, onions, peas, and garlic until the vegetables are tender.
Add the remaining 3 tablespoons of butter to the pot and let it melt. Sprinkle the flour over the mixture and stir continuously to create a thick roux. Cook for 2 minutes to remove the raw flour taste.
Gradually pour in the heavy cream, chicken broth, milk, while stirring constantly to avoid lumps. Continue stirring until the mixture thickens.
Add in the shredded chicken and mix well. Season the mixture with the fresh herbs, salt, garlic powder, onion powder, and pepper. Combine and simmer on low until mixture thickens.
Roll out one sheet of puff pastry and line a pie dish with it. Stretch the puff pastry and put if needed. 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.