Prepare pie toppers first. In a small food processor, combine the butter,flour,salt,cheese,and herb. Pulse until pea sized pieces are formed. Slowly add the ice water and continue pulsing until a dough ball is formed. Flatten into a disc shape and wrap in parchment paper or saran wrap. Chill for at least 30 minutes.
In a large dutch oven, over a low heat, melt the butter and oil. Add the onions,potatoes,celery,and carrots. Saute about 6 minutes,stirring frequently. Season with salt,pepper,and garlic.
Sprinkle with flour and stir until veggies are well coated.
Add the chicken broth and bring to a boil. Lower heat to a simmer and stir in the soup.
Cook over a low heat until the potatoes become tender. Stir in the soup,chicken,peas,and heavy cream. Continue to cook over a low heat for 5-10 minutes.
Bake the pie crust toppers while soup is cooking. Preheat oven to 375 degrees F.
Roll the dough out on a lightly floured surface to 1/4 inch thickness. Cut out desired shapes with cookie cutters or metal rounds. Arrange on a parchment lined baking sheet. Whisk together the egg and milk. Brush the pie cut outs. Bake for about 15 minutes or until golden brown.
To serve the soup, garnish each bowl with a few pie toppers and fresh parsley.