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Heat olive oil in a large pot over medium heat. Sauté onion until softened, about 5 minutes. Add garlic and cook 1 minute more.
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Add crushed tomatoes, broth, and sugar. Bring to a boil, then reduce heat and simmer 15 minutes.
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Tear basil leaves and stir into the soup. Blend with an immersion blender until smooth (or leave slightly chunky).
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Stir in heavy cream. Season with salt and pepper. Heat through on low for 5 minutes.
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Serve with grilled cheese sandwiches — it's the law in this house.