Step 1

Heat oil in a Dutch oven over medium-high. Add sausage, and cook, stirring often to break into pieces, until sausage is barely pink, about 4 minutes. Add tomatoes, onion, and garlic, and cook, stirring often, until vegetables are softened, about 4 more minutes. Add wine, and cook until reduced by half, about 2 minutes, scraping bottom of Dutch oven to release any browned bits. Add chicken stock and pepper, and bring to a boil. Add broken pasta, and stir, making sure pasta is mostly submerged. Reduce heat to medium; cover and cook until pasta is al dente, about 7 minutes.

Step 2

Remove from heat, and stir in arugula and vinegar. Toss until arugula is wilted, about 1 minute. Spoon 1 1/2 cups into each of 4 bowls, and top each bowl with basil and 1 tablespoon of cheese.