For the soup, clean and wash the leek and cut into rings. Peel and finely dice the ginger. Peel garlic and chop finely. Peel, wash and chop potatoes.
Heat 1 tablespoon of oil in a large pot. Sauté leek, ginger and garlic in it. Steam the potatoes briefly. Season with salt and pepper. Add coconut milk and 800 ml water. Stir in broth, bring everything to the boil. Remove the outer leaves from the lemon grass. Press the sticks a little bit and add them to the soup. Cover and cook over medium heat for 20-25 minutes.
Meanwhile, for the Gremolata, wash the lemon hot, dry it and finely grate the rind. Halve the lemon and squeeze it. Chop the pistachios and capers very finely. Wash parsley, shake dry, pluck off leaves and chop finely. Peel and finely chop the shallot. Mix everything with 4 tablespoons of olive oil and season with salt and pepper.
Remove the soup from the stove, remove the lemongrass. Remove 4 tablespoons of potato cubes from the soup. Finely puree the soup with a hand blender. Add the potato cubes again, season to taste and arrange the soup. Sprinkle with the Gremolata.