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 to combine. Add 3 cups vegetable broth, or enough to cover the contents. Increase heat to bring to the boil, then reduce heat to medium-low and simmer, partially covered, for about 35 minutes, until barley is tender. Add beans and kale; simmer gently for another 10 minutes. Warm remaining vegetable broth and add it as needed, 1 cup at a time, until you have a thick, soupy texture.

To serve, ladle stew into bowls and use a vegetable peeler to grate a few slices of pecorino over each.