Rinse the soaked chickpeas, cover with water, and cook with the potato until tender. Remove the outer skin of the leeks, slice lengthways from the root up, wash carefully and slice finely.
Warm a thick-bottomed pan, and add the tablespoon of oil and the knob of butter. Add the leeks and garlic to the pan, and sweat gently with a good pinch of salt until tender and sweet. Add the drained chickpeas and potato and cook for 1 minute. Add about 2/3 of the stock and simmer for 15 minutes.
Puree half of the soup in a food processor, and leave the other half chunky. This gives a lovely smooth comforting feel but also keeps a bit of texture. Now, add enough of the remaining stock to achieve the consistency you like. Check for seasoning, and add Parmesan, to taste, to round off the flavors.
This is classy enough for a starter, but I like it best for lunch in a big bowl with a good drizzle of my best peppery extra-virgin olive oil, a grinding of black pepper and an extra sprinkling of Parmesan.