Slice sausage into very thin pieces (I sometimes use a food processor for this step) and saute with onion until onion is transparent.
Add minced garlic and sliced zucchini.
Then add carrots.
Shred or chop cabbage finely, then add that to the mixture.
Saute a few minutes longer, then add beef stock and bring to a boil. Add seasonings and tomatoes, reduce heat, and simmer for at least an hour.
Notes
I usually put this soup on to cook during morning recess, then let it simmer while I read aloud to the children. Two chapters later, I add the great northern beans (final step) and dish it into bowls.