Chop onion, carrots, and celery. Set aside. Chop cooked meat into bite size pieces. Set aside. In large saucepan, melt 1/3 cup butter over medium heat.
Stir in flour, onion, and spices. Cook stirring until mixture is bubbly. Remove from heat. Stir in broth and milk. Heat to boiling, stirring constantly. Boil and stir 1 minute. Stir in meat, peas, carrots, and celery. Remove from heat.
** To make homemade pie crust (store bought you could skip these steps) Prepare the pie crust by mixing flour and 2/3 cup butter. Use a pastry blender or criss-cross two butter knives together to create a crumbly texture.
Add cold water in one tbsp at a time, fluffing with fork, until crust can form a ball that is not too wet, but holds together. Spread flour onto surface, take half of the crust dough and roll out into a large round shape big enough for your pie plate.
Place dough into your pie plate, pressing in to form around the inside as needed. Pour pot pie mixture onto pie crust. Set aside. Roll other half of the dough into another large round shape.
Place dough on top of pot pie mixture to create the top layer of the pot pie. Crimp the edges using your thumb and forefinger. Use a knife to cut small slits in the top to allow steam to escape.
Place pie on a baking sheet in case it overflows. Bake at 400° for 40-45 minutes or until golden brown.