Season chicken breasts with salt and pepper.
Add chicken broth and chicken breasts to a pan.
Bring to a boil, then turn heat down and let chicken simmer on low covered until cooked through.
Set chicken breasts aside to cool and strain chicken broth if needed.
Once chicken breasts are cooled, dice or shred.
Preheat oven to 425 degrees.
Melt butter in a large saute pan of medium low heat.
Add onions and carrots and cook over medium low heat until softened, but not browned.
Sprinkle in flour and continue cooking about a minute more.
Stir in chicken broth, bring to a boil and let simmer until thickened.
Stir in cream, chicken and frozen peas.
Season with one teaspoon of salt and plenty of freshly ground pepper. Taste and adjust seasoning as needed.
Once filling is prepared, lay pie crust dough on 9 inch glass pie dish.
Fill with half of filling, then add top pie dough.
Fold edge of top dough under bottom pie dough and pinch together to close.
Cut slits in top of pot pie to let vent.
Beat one egg with a tablespoon of water and brush over top of pie dough.
Place pot pie on a baking sheet to catch any drips.
Bake on lower rack of oven for 40-45 minutes until pie crust is browned.
If top crusts browns too quickly, lightly cover with aluminum foil.