Warm the olive oil in a soup pot over medium heat, then stir in the onions and garlic, followed by the cabbage and salt.
Cook for about 5 minutes, until just starting to soften, then add the beans and broth.
Bring to a simmer, then cover and cook for 30 minutes, or until the vegetables are tender and the broth is flavorful.
Remove from the heat and add the cheese a handful at a time, stirring until it melts into the broth.
Taste and season with additional salt, as needed, and a few grinds of pepper.
Serve hot, topped with breadcrumbs or croutons, if desired.
