Heat oil in a large Dutch oven over medium-high heat. Add sausage; cook, stirring to crumble, until browned and no longer pink, about 5 minutes. Add onion and carrot; cook, stirring occasionally, until the onion is translucent, about 4 minutes. Add garlic and Italian seasoning; cook, stirring constantly, until fragrant, about 1 minute.
Stir in broth and tomatoes; bring to a boil over high heat. Reduce heat to medium to maintain a simmer; cook, covered, until the carrots are tender, about 5 minutes.
Uncover and return to a boil over high heat. Add tortellini. Reduce heat to maintain a gentle boil; cook according to package directions.
Reduce heat to medium-low; stir in spinach and half-and-half. Stir gently until the spinach wilts, about 1 minute. Ladle the soup into 6 bowls. Additional reporting by Carrie Myers and Jan Valdez
