Core and wash cabbage. Separate leaves, and cook in boiling water 3 minutes or until limp. Drain and set aside.
Sauté onion and garlic in hot shortening in a large skillet until tender. Add meat and rice; cook until meat is browned, stirring to crumble.
Place 2 tablespoons meat mixture in center of each cabbage leaf; fold ends of leaves over, and fasten with wooden picks. Place in a Dutch oven. Add water, tomato sauce, salt, and pepper. Bring to a boil. Reduce heat; cover and simmer 1 to 1 1/2 hours. Remove rolls to a serving platter; serve with sauce.