Quickly rinse the chickpeas and leave to soak in cold water for at least 12 hours. Change the water several times.
Sauté the peeled clove of garlic with the sprig of rosemary for 5 minutes in 2 tablespoons of oil. Remove the garlic, pour the well-drained chickpeas into the saucepan, and leave them for a few minutes to absorb the flavor.
Cover the pulses with plenty of water, bring to the boil and cook for about 2 and a half hours, or until they are soft. In the meantime, take the chestnuts and use a sharp knife to make an incision down the back. Then roast them in the oven. When they are well cooked, peel the shell and remove the outer membrane.
Add salt when they are nearly cooked. Use an immersion blender to puree the chickpeas and chestnuts in the stock. Pour the cream into individual dishes and season with extra virgin olive oil.