Step 1Heat the oil in a large pot over high heat. When hot, add the prosciutto. Cook, stirring often, until the prosciutto is browned and crispy on the edges, about 2 minutes. Add the onions, celery, fennel, mushrooms, 1 tablespoon of garlic and the rosemary. Cook over medium-high heat, stirring often, until the onion is softened, about 7 minutes.
Step 2Add the beans, tomatoes, broth, red pepper flakes and pepper to taste. Mix. Bring to a boil, then reduce the heat to a simmer; cook, partially covered, stirring often to avoid sticking, for about 45 minutes. Stir in the pasta and remaining 1 teaspoon of garlic; cook 5 minutes more. Taste; adjust seasonings. Be wary of adding salt as the cheese garnish adds more. (This can be made 3 days ahead and refrigerated or frozen up to 1 month. It's OK if the soup becomes very thick. To serve, gently reheat, adding water as needed to thin; keep the consistency thick but with some visible liquid. Taste; adjust seasoning.) Stir in the arugula; cook 30 seconds. Serve hot, passing the cheese separately.