Peel and chop the onion, garlic, celery and potato. Wash and drain the potato and celery. Heat 1 tablespoon of oil in a saucepan. Fry the potato, onion, garlic and celery for 4-5 minutes until transparent, add the stock and simmer covered for 20-25 minutes.
Grate the cheese, sprinkle it as 4 small oblong cookies on a baking tray lined with baking paper and press it slightly flat. Bake in the preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: level 2) for 8-10 minutes, remove from oven and allow to cool.
Wash the dill, shake dry, pluck flags, except for something to garnish, from the stalks and chop. Mix dill, 1 tablespoon of oil and crayfish, season with a little salt. Pour cream into the soup, puree finely.
Pour the soup through a sieve, season with salt, pepper and a little sugar. Serve the soup, add crayfish to the soup and garnish with the remaining dill. Add Parmesan chips.