Preheat the oven to 400 degrees Fahrenheit.
Roll out one of the pie crust and place it into the bottom of a 9inch pie pan. Place it in the fridge until you're ready to fill it up, and set your second pie crust aside.
Add the butter to a large skillet over medium heat.
Add in the potatoes, carrots, onions, and celery and sauté them in the butter for about 10 minutes, stirring occasionally, until they are slightly tender.
Stir in the flour, rosemary, thyme, and salt, and pepper, and coat the vegetables with them.
Slowly pour in the chicken broth and heavy cream, whisking the flour mixture into them to get rid of any lumps.
Continue to let the mixture simmer for about 10 more minutes, or until the sauce has thickened nicely**
Add in the cooked chicken, and frozen peas or corn if desired, and stir them into the gravy to warm them up.
Spoon the chicken mixture into the prepared pie crust.
Roll out the top pie crust and place it over the pie. Use your fingers or a fork to pinch the edges sealed. Cut a few slits in the top of the crust to vent.
Whisk together the egg and water in a small bowl, and use a silicone brush to brush the edges and top of the pie crust with the egg wash.
Bake the pie in the preheated oven for 40 to 50 minutes, or until the crust is nice and golden and the insides are bubbly.
Bake the pie in the preheated oven for 40 to 50 minutes, or until the crust is golden brown and the filling inside is bubbly. **
Remove the pie from the oven and let it cool for about 10 minutes. Then slice it up and serve.