Bess Feigenbaum’s Cabbage Soup

In a 6-quart pot over medium-low heat, heat olive oil and add garlic. Cover and cook until garlic is tender but not browned, about 2 minutes. Add onion, and sauté until translucent. Add 3 cups water, carrots, tomatoes and purée, tomato paste, ketchup, brown sugar and bay leaf. Simmer at a lively bubble for 10 minutes, then crush whole tomatoes with potato masher or fork. Continue to simmer until carrots are tender, about 10 minutes. Discard bay leaf.
Using an immersion blender, or working in batches with a stand blender, process mixture until it is coarse, but not puréed. Return sauce to pot and add lemon juice, cabbage ribbons and remaining 3 cups water. Place over medium-high heat and cook at a lively simmer until cabbage is cooked to taste, from al dente to meltingly soft, 1 to 2 hours. Add 3 to 6 cups water to thin to desired consistency. Ten minutes before serving, stir in raisins and a few twists of black pepper.