Preheat oven to 375-degrees.
Add one of the pie crusts to the bottom of a prepared pie plate which has been sprayed with cooking spray. Set aside.
Melt the butter in a large skillet. Add the flour and whisk to combine. Cook for 1-2 minutes over medium heat.
Add the chicken broth to the skillet and whisk, cooking until the mixture thickens.
Add the cooked rice, cooked chicken, vegetables, scallions, half and half, salt and pepper to the skillet. Stir well and heat through.
Spoon the chicken and rice mixture into the prepared pie plate and top the mixture with the second pie crust. Use a paring knife to cut slits in the top crust for the steam to escape.
Trim away the excess pie dough (save if you're decorating the pie), and crimp or fold the two crusts together to seal.
Use a paring knife to cut out some decorative carrot and pea shapes and add them to the top pie crust using a light touch of water, pressing gently. This step is optional.
Whisk the egg and 1 tablespoon of water and brush the egg wash over the top crust before baking.
Place the pot pie on a baking sheet and bake in a preheated oven for 30 - 35 minutes or until the pie crust is golden brown in color and the filling is heated through. *Note - if the pie crust browns too quickly, cover the pie with foil and continue baking for the specified amount of time.
Allow the pie to cool for 15 minutes before slicing.