Peel the potatoes, cut them in half (see note), and boil them in a large pot of salted water, about 20-25 min, depending on the size of the potatoes.
Meanwhile, wash the leeks (by cutting a slit through the length, and running under water thoroughly, and in-between the layers).
Thinly slice the leeks.
Heat 2 tbsp of butter (25g), add the leeks and cook over medium low heat, covered, stirring often, about 6 minutes, until softened.
Add the other 2 tbsp of butter, milk, salt and pepper to the leeks and stir. It should be very soupy. Turn off the heat.
When the potatoes are soft, drain them and mash them with a potato masher.
Pour the leek/milk mixture over the potatoes and stir. Adjust seasoning and add a pinch of nutmeg if you'd like,
Serve right away! Enjoy!