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Add the crushed tomatoes, onion, garlic, carrots, celery, broth, sugar, salt, pepper, and dried basil to your slow cooker. Stir well to combine.
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Cover and cook on low for 6–8 hours or on high for 3–4 hours, until the vegetables are tender.
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Use an immersion blender to puree the soup until smooth (or carefully transfer to a blender in batches).
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Stir in the cream and butter if using, and adjust seasoning to taste.
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If using fresh basil, stir it in just before serving.
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Serve warm, optionally topped with a drizzle of cream or a sprinkle of Parmesan cheese.er adding cream to keep it from curdling.