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Heat oil and butter in a medium size pan. Add garlic and sauté until soft and fragrant, about 3-4 minutes. Add chopped onion and continue to cook until onion is translucent, about 4-5 minutes longer.
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Add chicken broth, carrots, tomatoes, bay leaves, tomato paste, balsamic vinegar, sugar, salt and ¼ cup of the fresh basil leaves. Cook, uncovered for 25 minutes until carrots are very soft.
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Remove bay leaves and allow to cool slightly*, then transfer half of the contents to a blended, add remaining basil and blend until smooth and creamy. Transfer blended soup to a medium size bowl, then repeat blending with second half of soup . Return soup to pot and re-warm gently before serving. Serve hot in soup bowls.
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If desired, top each bow of soup with bite size pieces of fresh mozzarella, finely chopped fresh basil, a pinch of red pepper flakes, a few pine nuts and small fresh basil leaves for garnish.