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Heat a large soup pot over medium heat. Add the oil, onion, carrot, thyme, and rosemary. Cook until the onions are softened and starting to brown (about 5 minutes).
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Stir in the garlic and Swiss chard and continue to cook until aromatic (about 30 seconds). Add the stock, tomatoes, and acini de pepe. Bring to a simmer.
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Season with salt and pepper and cook until the ancini de pepe is al dente (about 10 minutes). Taste and adjust seasoning.
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Divide between 4 bowls and sprinkle with basil.