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Heat oil in a large vessel over medium heat until hot and rippling. Add onions and garlic, and cook, stirring frequently, until translucent, about 3 to 5 minutes. Add carrots, salt, and pepper, and cook until the vegetables are slightly tender, about 5 minutes.
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Add crushed tomatoes, basil, oregano, and bay leaf, cover, and reduce heat to low. Simmer for one hour, stirring occasionally, until thickened and the vegetables are completely tender.
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Stir in butter and brown sugar. Season with additional salt and pepper if needed. Remove and discard bay leaf. Using an immersion blender or food processor, blend the sauce until smooth.