Load the slow cooker: Add tomatoes with their juices, onion, garlic, carrots, tomato paste, broth, olive oil, salt, pepper, basil, oregano, and red pepper flakes if using.
Stir to combine.
Cook low and slow: Cover and cook on Low for 6–8 hours or High for 3–4 hours, until the carrots are very tender and the flavors are blended.
Blend until smooth: Use an immersion blender directly in the slow cooker to blend until silky. For extra smooth soup, blend in batches in a countertop blender, then return to the slow cooker.
Adjust the balance: Taste. If it’s too tangy, stir in 1 teaspoon sugar and a splash of cream.
If it needs brightness, add 1–2 teaspoons balsamic vinegar or lemon juice.
Finish with cream (optional): Stir in the heavy cream or half-and-half. Warm through for 5 minutes but don’t boil.
Serve: Ladle into bowls and top with fresh basil, a drizzle of olive oil, croutons, or grated Parmesan. Add a grilled cheese for classic comfort.