Cook them in a heavy-bottomed casserole or soup pot in butter at a moderate heat, taking time to slowly coax the sweet juices from the vegetable. It should take about 15 minutes. Meanwhile cook the 6 potatoes for 10 minutes in about 2 pints of water until soft. Take out the potatoes and reserve the cooking liquids.
Combine the cooked leeks, celery and onion, the potatoes and about half to three quarters of the cooking liquids into a blender. Add freshly ground black pepper, a pinch of nutmeg, and a couple of pinches of salt. Blitz the mixture until you get a smooth texture. If the mixture is too lumpy, add the remaining cooking liquids and blend further.
The next step requires patience. Pop open the blender lid sufficiently for you to drip stream into the blending mix FULL CREAM milk, with the blending running on low speed all the time. The whole idea is to achieve a creamy, smooth, texture in the soup.
Once done, pour the soup onto a soup serving bowl. Add a sprig of thyme or two, and drip in some nutty olive oil, and grind in some fresh black pepper. To add an Asian twist to this classical French favorite, you can add a drop or two of garlic oil, or even fried shallots.
If you don't like leeks, feel free to substitute with cauliflowers, artichokes, or even cabbages. Works the same way!
The soup keeps well overnight in the fridge. Because there's milk in the soup, make sure you put any leftover soup into the fridge immediately. For reheating, put the soup in an ovenproof pot (preferably enameled cast iron), and pop it into a pre-heated 150 deg C oven for 20-25 minutes, depending on the amount of soup you have.