Simmer the stock and barley in a large soup pot for 30 to 40 minutes.
While the barley is cooking, cook the onion in a non-stick skillet (with a lid) over medium-high heat until it begins to brown.
Add the garlic and mushrooms and a little salt and pepper, reduce the heat, cover, and cook, stirring regularly, for about 3 to 4 minutes.
Add the thyme and sherry and cook until the alcohol cooks off.
Once the barley is cooked, add the mushroom mixture to its pot along with the sliced cabbage and paprika.
Add the water to the pot.
Add the cannellini beans and simmer, covered, for about 30 minutes, until the cabbage is tender, adding extra water if it gets too thick.
Stir in the lemon juice just before serving and add more salt and pepper.