Preheat the oven to 350 and have your pie dough prepared*, either store bought or homemade
In a large skillet, melt the butter and add the onions, garlic, and chicken on medium heat. Stir until the chicken starts to brown. Add in the celery, carrots, pepper, thyme, and rosemary. Sprinkle the flour over the top of everything, stirring and cooking another 3-5 minutes
Pour the chicken stock and half n half over the chicken and vegetables and let simmer for about 10 minutes. The chicken should be cooked through and the broth should be turning into a thicker sauce
Using a small bit of butter, grease the bottom of the pie plate. Pour the chicken pot pie filling into the dish**. Beat the egg in a separate bowl
Roll the pie dough over the chicken filling, trimming excess around the edges. Either poke holes across the top with a fork or create an x in the middle with a knife. Brush the top of the crust with the egg wash
Bake for about 25 minutes, or until the crust is golden. I recommend placing a cookie sheet on the rack under the pie plate to catch any of the filling that may bubble up and over