In a large saucepan over medium-high heat, sauté olive oil, onions and garlic until soft, about 1 to 2 minutes. Add sausage and stir to break up. Cook until browned, about 5 minutes. Drain fat from sausage, as desired. Add chicken or vegetable broth, diced tomatoes, crushed tomatoes, tomato paste, basil, oregano, thyme, parsley and rosemary. Bring to a boil, then reduce heat to medium-low, cover and simmer for 20 minutes.