Pasta e Fagioli with Borlotti Beans

Name: Pasta e Fagioli with Borlotti Beans
Ingredients: 2 ½ pounds large tomatoes (4 to 5), such as beefsteak; 1 ½ cups shelled fresh borlotti beans (from about 1 pound in the pod); Coarse salt; 1 tablespoon extra-virgin olive oil, plus more for drizzling; 1 medium onion, diced (about 2 cups); 1 celery stalk, diced (about ½ cup); 1 medium carrot, diced (about ⅓ cup); 2 garlic cloves, minced (about 1 tablespoon); 3 -inch-long piece Parmesan rind or 1 slice salami; 3 sprigs basil; 2 cups water; 1 cup ditalini pasta; Freshly grated Pecorino Romano or Parmesan cheese, for serving