1 Brown the sausage: Heat the olive oil on medium-high heat in a large (8-quart), thick-bottomed pot. Add the sausage, breaking it up into pieces as you put it into the pot in a single layer.
When the sausage has nicely browned, remove it with a slotted spoon and set aside.
2 Sauté onions, garlic: Add the minced onion (save the sliced onion for later) and sauté for 3-4 minutes, stirring often.
Once the onions give up some of their water, use a wooden spoon to scrape up any browned bits from the bottom of the pot.
Add the minced garlic and cook for another 1-2 minutes.
3 Add wine, beans, boil, lower heat to simmer: Add the white wine and the beans and bring to a rolling boil. Reduce to a simmer. Cover and cook for 10 minutes. If you want, for a thicker base, use an immersion blender to blend some (or all) of the beans and onions.
4 Add water, stock, salt, cabbage, sliced onion, bay leaves sausage, then simmer: Add the water, stock, salt, cabbage, sliced onion half, bay leaves and browned sausage. Bring to a boil, reduce heat to a simmer. Cover and simmer for 10 minutes, then uncover and continue cooking until the cabbage is tender, about another 10-20 minutes.
To serve, sprinkle on chopped parsley and grated cheese.