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Preheat oven to 450˚F. Combine tomatoes, onion, garlic, oil, balsamic vinegar, salt, pepper and sugar in a large bowl. Stir gently with a large spoon or spatula to coat. Turn mixture out onto a rimmed sheet pan and arrange tomatoes cut side down. Nestle garlic cloves in the center of the pan. Be sure to scrape out all the good oil and juice in the bowl.
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Bake for 30 minutes, then flip tomatoes to opposite side and bake for another 10-15 minutes, until most of the liquid has been evaporated. Depending on the size of your tomatoes, cooking time can vary a bit so keep an eye on them at the end.
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Remove from oven and transfer the tomato mixture (and any liquid left in the pan) to a large soup pot or Dutch oven. Add the lentils, broth, tomato paste, bay leaves and salt. Bring to a boil, then cover and reduce to a steady low simmer. Cook for 20 minutes then remove from heat.
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Remove bay leaves and add basil to the soup. Then blend with an immersion blender or stand blender. If using a stand blender, allow the mixture to cool a bit before blending. It’s also a good idea to leave the center cap of the blender lid off and cover it with several layers of paper toweling. (If too much heat builds up in the blender container, it can cause an explosion.) Leave the soup a bit chunky, not super smooth.
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Taste and add a bit more salt, if needed. Serve soup hot topped with halved Ciliegine (see note below), cherry tomato halves and small fresh basil leaves. If your basil leaves are large, just slice them thinly. Drizzle each serving with a teaspoon of olive oil and a shower of fresh ground black pepper.