Preheat your oven to 425°F (200°C).
In a large skillet, melt the butter over medium heat. Add the diced onions and carrots and saute for about 8-10 minutes until they are soft. Add the mushrooms and garlic and saute for another 4-5 minutes.
Sprinkle the flour over the vegetables and stir continuously to create a roux, about 1 minute. Pour in the half and half and chicken broth, bring to a simmer and cook until mixture is thick like a gravy, stirring continuously, about 1-2 minutes.
Add the rosemary, thyme, oregano salt, pepper, garlic powder, and onion powder and stir to combine. Turn off the heat and add in the shredded chicken and frozen peas and mix well.
Line a deep pie dish with one of the pie crusts. Fill the dish with the chicken mixture. Place the second pie crust sheet over the filling and press the edges of the top pie sheet and the bottom pie sheet together to seal the pie. Use a sharp knife to cut 5 or 6 small slits in the top to allow steam to escape. Brush the top of the pie with the beaten egg.
Bake the pie in the oven for 30-35 minutes until the pie crust is golden brown and the filling is hot and bubbly. Allow the pie to rest for 15-20 minutes before serving.