Peel and chop the shallots. Peel and wash the potatoes and cut them into pieces of about 2 cm. Heat butter in a pot. Steam shallots until translucent. Add the potatoes and steam for about 2 minutes while turning.
Deglaze with broth and bring to the boil, cover and cook over medium heat for 10-15 minutes.
In the meantime wash and peel the apples. Cut thin slices from 1 apple around the core. Cut slices into fine sticks. Sprinkle with lemon juice. Core the remaining apple and dice. Wash basil, shake dry, remove leaves.
Add apple cubes to the soup and bring to the boil briefly. Finely puree the soup with a hand blender. Season with salt and cayenne pepper. Stir apple strips into the soup. Arrange in small bowls sprinkled with basil.