Heat butter in large, heavy skillet. Add onions, celery, and parsley. Cook over low flame for 5 minutes. Arrange rolled meat on bottom of pan. Cook uncovered for 10 minutes, turning two or three times so that meat rolls are whitened on all sides. Do not allow meat to brown.
Cover. Simmer for 1 hour, turning twice during the last half-hour of cooking.
Discard strings. Remove meat to heated serving dish and keep warm. Add consomme to pan. Bring to boil and cook for 5 minutes. Pour over meat.