Heat oil in a large pot over medium heat. Add onion and garlic; cook until soft, about 5 minutes. Stir in sausage and tomato paste; cook 3 to 4 minutes.
Add broth, diced tomatoes, tortellini, salt, and black pepper; bring to a boil. Reduce heat; simmer for 5 minutes. Stir in spinach; cook 3 to 4 minutes. Top servings with Parmesan cheese.
