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Rinse the soaked chickpeas, cover with water, add the potato, and cook with until tender, about 1 hour.
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In a large pot, heat the olive oil and butter. Add the leeks and garlic with a pinch of salt and sautee until tender.
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Add the chickpeas and potato and cook for 1 minute. Add about two-thirds of the stock and simmer for 15 minutes.
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Puree half the soup in food processor. Add remaining stock. Season with salt, black pepper and add grated Parmesan cheese.
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Ladle soup into serving bowls, drizzle with some olive oil, add ground black pepper, some more Parmesan cheese and serve.