TO MAKE THE CABBAGE ROLLS: Heat the oil in a skillet and saute' the onions until golden. In a large bowl, combine the ground beef with the eggs, water, rice, salt and pepper. Add the sauteed onions to the beef mixture and mix well. Set aside.
Core the cabbage and separate into leaves. Place the leaves in a large pot, cover with water, and bring to a boil. Reduce the heat and simmer for about 8 minutes. Drain and cool the leaves until they can be easily handled.
Cut the large leaves in half, removing the hard core. Place about 3 tablespoons of the meat mixture on a leaf. Fold the edges toward the center and roll up. Repeat until all the leaves are used. Place the the rolls in a large pot with the edges down, piling one on top of another, and separating them with a few of the small cabbage leaves.
TO MAKE THE SAUCE: In a saucepan, combine the tomatoes, tomato puree, water, onions, brown sugar, honey, lemon juice, ginger snaps, raisins, and salt. Simmer for 10 minutes, then taste and adjust the sweet and sour to your liking. Pour the sauce over the cabbage rolls, cover, and cook GENTLY on top the stove for 1 1/2 hours.