Once the onion is translucent, add the broccoli and hot stock to the pan, bring to the boil and cook until the broccoli stalk is just soft, this will take around 10 minutes. The broccoli should still be a lovely, vibrant green.
Remove the pan from the heat and blend the contents until they are silky and smooth. I like to use a stick blender for this.
Return the soup to the heat, add 200g of the cheese and heat until the cheese is melted and the soup is just below simmering.
Ladle into bowls, sprinkle the remaining stilton onto the soup and serve with fresh crusty bread.