Heat oil in a large pot over medium heat; add garlic cover and cook until soft.
Uncover, add the onion and sauté until translucent.
Add 3 c chicken broth, carrots, tomatoes and purée, tomato paste, ketchup, sugar and the bay leaf.
Bring to a boil then reduce to a simmer and cook for 10 minutes.
Crush the whole tomatoes and continue to simmer until carrots are tender (10 more minutes).
Discard bay leaf and, using an immersion blender, blend until slightly chunky (this step is not necessary, texture is good). As an alternative you can pulse the tomatoes in a food processor a couple of times before adding or use a can of crushed or cubed tomatoes. All work nicely.
Add lemon juice and cabbage and remaining 3 cups chicken broth (there will be a LOT of cabbage, but it will cook down).
Again, bring to a boil, then reduce heat and simmer until the cabbage is done however you like it (1 hour for al dente,2 hours for soft, or anywhere in between).
Add additional chicken broth, if necessary, until the soup reaches your desired consistency.
Add the raisins 10 minutes before serving.
Season with salt and pepper.
Serve topped with a dollop of sour cream or Greek yogurt.