Combine ground beef, eggs, rice, ketchup and mix thoroughly.
Cut out the core of the cabbage and remove any damaged outer leaves. Immerse the cabbage in boiling water and remove leaves as they become loose.
Divide ground beef mixture equally on 16 cabbage leaves. Roll leaves loosely around meat mixture, allowing for expansion. Tuck in the ends as you roll. If you have any remaining cabbage, roughly chop it and place in the bottom of a large roaster or a Dutch oven, add cabbage rolls, seam side down.
Combine crushed tomatoes, tomato sauce and brown sugar. Pour this mixture over the cabbage rolls.
Bake at 350°F for about 3 hours. Cover for the first hour, then bake uncovered for the remaining 2 hours. Baste frequently.