In large pot over medium heat, add olive oil and sauté onion, garlic, thyme, and bay leaf until softened, about 5 minutes. Add carrot, celery, and fennel and cook for a further 5 minutes. Add salt, pepper, and barley and stir thoroughly.
Pour in the vegetable broth, bring to a boil, then reduce heat and simmer for 30-40 minutes, or until the barley is tender.
Stir in the beans and kale and cook until the kale is wilted, about 5 minutes.
Serve immediately, topped with grated Pecorino Romano cheese.