Sauté the cleaned, washed and finely chopped carrots, celery and onion in 1/3 of the butter until soft. Add 3 1/3 cups (800 ml) of hot water, add the cleaned and chopped spinach and boil. Bake the flour in a small bowl and add the second third of the pre-melted butter.
Remove the dish from the heat before it starts frying and dilute it with 2 cups (500 ml) milk and 2/5 cup (100 ml) of broth from the boiling vegetables.
For thickening, set aside 2/5 cup (100 ml) milk. Pour thus prepared sauce over the vegetables, season with salt and let it come to a boil. Then strain through a colander and thicken with the egg beaten in the set aside milk and season with the remaining 1/3 of the butter.
Optionally, serve the soup with croutons.