Melt the butter in a large pot, add chopped onion, season with salt and pepper, and cook over medium heat until translucent. Add celery and carrots and cook for 2 minutes. Sprinkle in flour and cook for 2 more minutes, adding a splash of broth if it looks too dry. Add chicken stock and bring to a simmer. Add potatoes and spices and simmer until mostly tender (but not fully cooked), about 15 min. Preheat oven to 350 degrees while the potatoes are cooking. Stir in turkey, parsley, and peas. Taste and adjust seasonings to your preference.

Pour mixture into a baking dish sprayed with cooking spray. Sprinkle a little flour on your work surface and roll out the crescent rolls so that it's about the same size as your baking dish (you can cut a little off the end and piece it back on the side if needed). Lay the dough on top of the baking dish and and brush with egg. Cut a few slits in the top of the dough to let steam escape and bake for 25-30 minutes until crust is deeply golden. Top with fresh parsley or chives if desired, and serve!