Heat olive oil in a large pot over medium heat. Add onion and garlic, and saute five minutes or until softened. Add tomato, and cook 1 minute. Stir in broth and rosemary, and bring to a boil; reduce heat, and simmer, covered, five minutes. Add pasta, stirring to blend, and simmer five to six minutes more.
Add spinach, salt, and pepper. Simmer, stirring often, three minutes or until spinach is wilted and pasta is just tender,. Ladle soup into bowls, and sprinkle with cheese or stir in a spoonful of pesto.