In a large skillet, heat oil over medium-high heat. Add onion and carrot; cook and stir until crisp-tender, 5-6 minutes. Add garlic; cook 1 minute longer. Transfer to a 6- or 7-qt. slow cooker. Add the tomatoes, broth, sugar, basil and bay leaf. Cook, covered, on low until vegetables are tender, 6-7 hours.
Stir in tortellini. Cook, covered, on high 15 minutes. Reduce heat to low; stir in cream until heated through. Discard bay leaf. Serve with Parmesan cheese and basil. Freeze option: Before stirring in sour cream, cool soup and freeze in freezer containers. To use, partially thaw in refrigerator overnight. Heat through in a saucepan, stirring occasionally, adding sour cream as directed.
