In a medium bowl, combine the lean ground beef with plain bread crumbs, dry onion soup mix, large egg, and milk. Divide into eight portions and form your patties. Place patties on a baking dish or plate and season with salt and pepper, then dust with flour.
Heat a large skillet or frying pan over medium heat, and melt butter. Add patties to the heated skillet or frying pan (seasoned side down) and season the upward facing side of your patties, then dust with flour. Brown both sides of the patties and remove from heat.
In your slow cooker, combine the can of condensed cream of chicken soup, worcestershire sauce, au jus gravy mix, and beef broth, Whisk all of the sauce ingredients together until smooth.
Place the browned patties into your slow cooker (about two layers) so that they are covered with the sauce. Add sliced mushrooms and chopped parsley.
Cook in your slow cooker on high for two hours or on the low setting for four hours (or until well done).