Slit the leek lengthwise, rinse thoroughly, clean and cut into fine rings. Also use the light and medium parts. Remove the skin from the potatoes, rinse and cut into small cubes.
Melt the butter in a large saucepan, but do not let it brown. Sauté the leek and potatoes in it over medium heat for about 2 minutes, stirring continuously.
Pour in the clear soup and let it bubble up. Cover the lid and simmer over medium heat for 15 minutes until the potatoes are soft.
In the meantime, rinse the parsley, toss dry and chop finely without the coarse stems. Remove the rind from the gorgonzola and dice.
Mix the parsley and the gorgonzola into the soup. Stir the cheese into the soup until it melts. Season the soup with salt and freshly ground pepper to taste.