Make a batch of All-Butter Pie Crust and refrigerate for several hours to chill.

In a large skillet, melt butter over medium heat. Add chopped carrots, onions, and celery. Cook for 5 - 8 minutes, until softened.

Sprinkle in ¼ cup all-purpose flour and cook, stirring constantly, for 2–3 minutes to eliminate the raw flour taste. Add chicken broth, whisking until smooth. Stir in herbs and heavy cream. Reduce heat to medium-low and simmer for a few minutes until thickened.

Stir in cooked, chopped chicken and frozen peas. Season with salt and pepper to taste. Remove from heat and let the filling cool slightly while you roll out the dough.

Preheat the oven to 400°F (200°C).

Roll out one half of the refrigerated pie crust and place it in a standard 9-inch pie plate. Trim any excess dough. Roll out the second half and set aside.

Pour the chicken pot pie filling into the bottom crust and smooth the top. Cover with the second crust, trim and fold the pie crust edges under, then crimp to seal edges. Cut a few small slits in the top to allow steam to escape.

Using a pastry brush, brush the top of the crust with heavy cream. Place the pie on a cookie sheet to catch any drips that may happen while the pot pie bakes. Bake for 40 - 45 minutes, or until the crust is golden brown.

Let the pie rest for 10 - 15 minutes before slicing. Serve and enjoy!