In a large bowl, mix first 8 ingredients; mix well. Add the beef and mix well. Form 8 patties. Roll in flour. Place on greased baking pans. Bake, uncovered for 15 minutes; turn and bake 10 more minutes.
SAUCE: Melt butter in saucepan. Stir in flour, thyme, salt and pepper. Slowly add broth and milk; bring to a boil. Serve over patties.