Slowly melt the butter in a pot until golden brown. Add the flour and lightly toast it while stirring continuously, until it develops a delicate nutty aroma. Gradually pour in the hot vegetable broth, stirring well. If any lumps form, briefly blend the soup with a hand blender until smooth.
Add the bay leaves and let the “Brennsuppe” simmer gently for about 10 minutes. Finally, slowly stir in the egg, season with salt and pepper to taste, and serve hot.
TIP: Cooked Borlotti beans or small pasta shapes are also delicious in “Brennsuppe”.