Warm the oil in a large soup pot over medium heat. Add the onion, celery, and carrots and cook until tender, 5 to 6 minutes. Add the garlic and cook for 1 minute. Add the broth and bay leaf, cover the pot, and bring the liquid to a boil over high heat. Stir in the wheatberries, return the broth to a boil, and then reduce the heat to low, cover, and simmer until the wheat berries are tender, 35 to 40 minutes.
Remove and discard the bay leaf. Transfer about 3 cups of soup (mostly solids) to a blender and puree until smooth. Return the puree to the soup pot and add the beans, kale, salt, pepper, and 2 tablespoons of the rosemary. Cook until the kale is tender, about 10 minutes. Stir in the vinegar.
Divide the soup among eight bowls and garnish with the cheese and remaining 1 tablespoon of rosemary. Serve with the toasted bread slices.
Tip: For extra flavor, add the leftover rind from a wedge of Parmesan to the soup along with the broth. Then discard it along with the bay leaf.