In a large pot, heat the oil. Add the celery, carrots, and onions; cook over moderate heat, stirring occasionally, until softened, 8 minutes. Stir in the garlic, paprika, and crushed red pepper and cook until fragrant, 2 minutes. Add the tomatoes, kale, thyme, and rosemary sprigs and the bay leaf and cook, stirring occasionally, until the tomato juices have evaporated, 5 minutes. Season with salt and black pepper.

Add the stock and beans to the pot; simmer over low heat, stirring occasionally, for 30 minutes. Discard the rosemary and thyme sprigs, and the bay leaf. Stir the vinegar into the soup and season with salt and black pepper. Ladle the soup into bowls, sprinkle with the pecorino, and serve.

Crusty bread.