Cook the broccoli in the vegetable stock. Put a few small florets aside and puree the soup. Add the grated Emmentaler cheese and the grated potatoes. Bring the soup to the boil, stirring constantly, until the cheese is dissolved. Remove the soup from the heat, mix with the egg yolk and season well.
Dice the toast and toast in the garlic butter until golden.
Garnish the soup with the broccoli florets and croutons.