Wrap cabbage leaves in plastic wrap or moist paper towels and microwave on HIGH for 2 minutes, until soft. Cut off the thickest, white portion of the spine of each leaf to make leaves pliable and easy to fold; set aside.
Combine beef, rice, water, bread crumbs, carrot, onion, garlic, egg white, salt and pepper in a large bowl; mix well.
Spoon about 1/4 cup of beef mixture onto center of each leaf. Fold up bottom of leaf to cover filling, tuck in sides and then continue rolling to make loose rolls (rice will expand during cooking so it is important not to roll them too tightly).
Heat oil in a large stockpot over medium-high heat; add rolls and sauté until golden brown on all sides, turning frequently, about 5 minutes. Add tomatoes and bring to a simmer. Reduce heat to low, cover and cook until cooked through, checking pot every 15 minutes and stirring to prevent sticking, about 1 hour. (If sauce thickens or reduces, add water.) Yields 2 rolls per serving.
