Remove core from cabbage. Steam 12 large outer leaves until limp. Drain well.
In a bowl, combine ground beef, rice, onion, egg and seasonings; mix well. Put about 1/3 cup meat mixture on each cabbage leaf. Fold in sides, starting at an unfolded edge, and roll up leaf completely to enclose filling. Repeat with remaining leaves and filling. Place rolls in a large skillet or Dutch oven.
Combine tomato sauce, brown sugar, water and lemon juice or vinegar; pour over cabbage rolls. Cover and simmer for 1 hour, spooning sauce over rolls occasionally during cooking.