Cook carrots and potatoes in water about 10 minutes. drain.
Melt butter in pan. stir in flour until well combined. add chicken broth, thyme, & salt and pepper, until sauce is creamy. Bring to a boil for 2 minutes until thickened. set aside.
In a large bowl, stir together the drained carrots and potatoes, white sauce, and all other ingredients.
Transfer mixture to a greased 2-quart pie dish or 8x8 dish. (if using a double crust, the dish does not need to be greased.) Top with pastry. Cut slits in top and brush with milk.