Heat the olive oil in a large pot over medium heat. Add the onion and cook until softened, about 5 minutes. Add the garlic and cook for 1 minute more.
Add the mushrooms and cook until browned, about 5-7 minutes.
Add the vegetable broth, barley, cannellini beans, cabbage, thyme, and smoked paprika. Bring to a boil, then reduce heat and simmer for 45-60 minutes, or until the barley is tender.