Heat the oil and butter in a saucepan.
Add the garlic and onion and sauté for 2-3 minutes, or until soft.
Add the broccoli and cook for 1-2 minutes.
Add the hot chicken stock. Bring to the boil then simmer for 4-5 minutes, or until the broccoli is tender.
Pour the soup into a blender or food processor and mix until smooth. Season with salt and freshly ground black pepper.
Place the egg yolk and cream into a bowl.
Add the hot soup and stir until the soup thickens slightly.
Crumble over the Stilton and serve hot.