Peel, wash and possibly halve the potatoes. Peel and halve the onion. Heat butter in a pot. Sauté the onion halves in it and take them out. Deglaze with broth and bring to the boil. Add potatoes and caraway seeds and cook for about 20 minutes.
In the meantime, quarter the peppers, remove seeds, wash and cut into bite-sized pieces. Add 5 minutes before the end of the cooking time. Wrap ham loosely around the Grissini sticks. Wash chives, dab dry and cut into small rolls. Season soup with salt and pepper. Arrange soup and ham grissini