Clean, wash, dry and cut leeks into rings;
Peel, wash, dry and cut potatoes into cubes;
In a large pot, melt 2 Tbsp (30g) of butter, then add the leeks and washed thyme. Sauté them over high heat and stir with a wooden spoon. If you opt for parsley or chives, add them at the end of the cooking;
Pour in about 1 liter (4 cups) of water; add a pinch of salt and some freshly ground pepper;
Bring it to a boil, turn the heat to low and simmer for about 30 minutes; partially cover the pot;
Meanwhile, simmer the milk for a few minutes;
Blend the soup with an immersion blender until creamy;
Pour in the warm milk; bring it to a boil again; let simmer for a few minutes and turn off the heat;
Remove it from the heat and add the remaining 2 Tbsp (30g) of butter,
Serve it warm with croutons; for more flavor, sprinkle grated Parmesan cheese on top.
When finished eating, divide the cooled soup into small serving containers and freeze.