Combine beef, onion, parsely, Worcestershire, basil, marjoram, salt and pepper in large bowl.
Remove one-fourth of the mixture to bowl. Mix in cooked rice. Shape into 4 equal patties; divide remaining meat mixture into patties. Freeze for up to 3 months.
Broil patties 3 inches from heat for about 14 minutes, turning over halfway through cooking. Serve on roll with cheese and tomato.
Heat butter in nonstick skillet over medium heat. Add mushrooms, onion; saute 8 minutes or until softened and mushrooms have released their juices. Combine beef broth and flour in small jar with tight-fitting lid. Stir into skillet; cook, stirring, 2 minutes or until thickened. Season with salt and pepper. Spoon over broiled beef patties from above. Makes 4 servings sauce (1-1/2 cups).