Preheat oven to 425˚F
In a dutch oven, melt 6 Tbsp butter. Add diced onions, peas, and carrots and saute 8 minutes over medium heat until soft.
Add minced garlic, poultry seasoning, chopped rosemary, and chopped thyme and saute another 5 minutes
Add 1/3 cup flour and stir constantly for 2 minutes. Add 2 cups of broth and 1/2 cup heavy cream then bring to a simmer and cook 1 minute or until mixture is a thick gravy consistency. Add salt and fresh black pepper to taste.
Add shredded cooked chicken. Stir to combine then remove from heat and cool slightly while you roll out the crusts. Roll 1 pie disk in a pie dish. Spoon the pie filling over the bottom crust.
Unroll the second disk of pie dough and place over the pie filling. Fold the excess dough behind the bottom crust then crimp the pie crusts with a fork together to crimp/seal. Use a sharp knife to cut 5 small slits in the top to allow steam to escape. Brush the top of the crust with the beaten egg and sprinkle lightly with kosher salt and fresh pepper.
Bake for 30-35 minutes or until top crust is golden brown. Once out of the oven, let cool slightly before slicing.
I normally use a rotisserie chicken and use all of the removed meat in the pie. I also like to set aside the bones and use them to make a bone broth (see earlier in the post for how I do that). Instead of homemade bone broth, you could alternatively just use store bought chicken broth though!