1. Preheat the oven to 180 degrees and prepare the broth. Cut the leek into thin slices. Peel the potatoes and cut them into small pieces.
2. In a soup pot, heat the butter and sauté the leek for 3 to 4 minutes over medium-high heat. Add the potato pieces, continue cooking for 2 to 3 minutes, and add the broth. Let the soup simmer for 13 to 15 minutes.
3. Meanwhile, crush or finely chop the garlic and roughly grate the Parmesan cheese. Mix the two in a bowl. Cut the ciabatta into slices, place them on a baking sheet lined with parchment paper, and sprinkle them with the garlic and Parmesan mixture. Bake the crostinis for 6 to 8 minutes or until crispy.
4. Meanwhile, finely chop the chives and cut the lemon into quarters.
5. Blend the soup using an immersion blender, season generously with pepper, and add salt if necessary.
6. Serve the soup in bowls and pour a generous spoonful of fresh cream into each one. Garnish with chives and serve with the crostinis and a lemon quarter.