Pound the meat slices lightly with a mallet or the flat side of a knife. Place one carrot strip and one sliver of garlic in the center of each. Sprinkle lightly with rosemary. Roll the slices and tie with string. Dip the rolls into flour.
Heat the oil in a skillet and brown the meat on all sides. Add remaining ingredients except parsley, and cover. Simmer for forty-five minutes, or until meat is tender.
Remove the beef rolls to a serving dish and strain the gravy over them. Sprinkle with parsley.