Melt butter in a large skillet or stockpot.
Add sliced carrots, celery, and onion, and cook on medium heat for 3-4 minutes.
Whisk flour into the vegetable butter mix. It will turn a bit lumpy.
Slowly add the heavy cream while stirring constantly. The cream will start to thicken.
Add chicken broth, herbs, salt, and pepper and continue stirring.
Add chicken and stir. The broth should be thickening.
Add the peas and stir.
Taste and add additional salt and pepper if needed.
Preheat oven to 425°.
Spray ramekins or a large pie pan with non-stick spray and fill with the chicken vegetable mix.
Roll out refrigerated pie crust dough and cut circles just a bit larger than the ramekins or pie pan (if you are making 1 large pot pie).
Place pie crust over ramekins or pie pan and press the sides to seal.
Brush the tops with egg whites.
Cut a few slices in the top of the pie crust to allow steam to escape while baking.
Bake for 25-30 minutes.
Let sit for 5 minutes before serving.