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