Heat olive oil in a skillet over medium heat. Add chopped onion, garlic, and carrots. Sauté until softened, about 5–7 minutes.

Transfer sautéed vegetables to Crockpot. Add canned tomatoes, tomato paste, broth, salt, pepper, and sugar (if using). Stir to combine.

Cover and cook on low for 6–8 hours or high for 3–4 hours.

Use an immersion blender to puree the soup until smooth (or blend in batches).

Stir in cream or coconut milk if using, then mix in chopped basil. Adjust seasoning to taste and serve warm.