For the soup, clean the leek, cut lengthwise, wash thoroughly and cut into small pieces. Peel and chop the garlic. Heat 1 tablespoon of oil in a saucepan. Stir-fry the leek and half the garlic for about 5 minutes.
Peel, wash and chop the potatoes. Add frozen peas, stock and 1⁄2 l water. Bring everything to the boil and simmer covered for about 20 minutes until the potatoes are soft.
For the pistou mint, wash, shake dry and pluck the leaves. Grate cheese finely. Finely puree the cheese, mint, rest of garlic, lemon juice and 60 ml olive oil with a hand blender. Season with salt and pepper.
Finely puree the soup with a hand blender, mixing in approx. 1⁄4 l water. Bring to the boil again, stirring frequently. Season to taste with salt and pepper. Distribute on soup bowls. Add a little pistou, add the rest.