Crumble the sausage into a large cold pot. Cook over medium-high heat, turning occasionally, for about 3 minutes, or until browned. Remove with a slotted spoon, set aside. Pour off and discard any drippings. Add the garlic and sage.
Cook for about 1 minute, or until fragrant. Add the beans, broth and water. Increase the heat to high and bring just to a boil. Scrape up the browned bits at the bottom of the pot.
Reduce the heat to medium-low. Cover partially and simmer for 15 minutes.
Transfer about half of the beans and enough broth to cover, to a blender or food processor. Purée and return to the pot. Add the macaroni and the reserved sausage.
Simmer for about 5 minutes, or until the pasta is al dente. Stir in the spinach, vinegar, salt and the pepper. Sprinkle with Pecorino Romano at the table.