Peel, wash and roughly grate the carrots and celery. Heat the butter and sauté the vegetables with the sugar in them. Deglaze with the broth and simmer for 15 minutes. Add creme fraiche and puree with a hand blender. Season to taste with salt and pepper.
For the pesto, put the parsley, thyme, parmesan and pine nuts in a tall mug and puree with the hand blender. Gradually add the oil (if you want it to be quicker and easier, you can also buy ready-made pesto).
Put the soup in plates and spread the pesto on top.