Clean the leeks: Wash them on the outside, top, and tail them. Cut and discard the last inch (2 cm) or so of the dark green ends; they are usually wilted.
Slice the leeks lengthwise, starting at the transition between the white and the green part and moving the knife towards the top of the plant.
Fan open the layers without taking the leek apart and rinse under cold running water until all the dirt is removed.
Chop the leeks.
Potatoes: Peel and wash them. Cut them into bite-sized chunks.
Sauté: Melt the butter, add the prepared vegetables, minced garlic, dried herbs, and a pinch of salt. Sauté on medium-low heat for 8 minutes, stirring every 2 minutes or so.
Simmer: Add the stock or broth, bring to a boil, and cook on low heat for 15-20 minutes until the potatoes are soft.
Adjust the taste with a few gratings of nutmeg, salt, and lots of freshly ground black pepper.
Optional: Leave the soup chunky or blend it to your liking using an immersion blender. You can blend it only partially or blend it until creamy (Notes 5,6).