Combine beef, onion, parsley, Worcestershire, basil, marjoram, salt and pepper in large bowl.
Remove one-fourth of mixture to bowl. Mix in cooked rice. Shape into 4 equal patties; wrap in freezer wrap; freeze for up to 3 months. Thaw in refrigerator.
Stir eggs, bread crumbs and milk into remaining beef mixture until blended. Divide into 3 equal batches. Flatten; wrap batches separately; freeze for up to 3 months. Thaw in refrigerator. Makes 4 burger patties and 3 batches (12 servings) ground beef.