Bring the milk to the boil then remove from the heat. Crumble the stilton into the milk, cover with a lid and leave to infuse. Peel and roughly chop the onions.
Melt the butter in a deep pan and add the chopped onion. Fry gently over a moderate heat for about 10 minutes until the onion is glossy and sweet smelling. Separate the leaves of the sprout tops, pick off the whole sprouts, set aside and finely chop the stems.
Add the stems and combine with the onion. Finely shred the sprout tops, stir into the onion and cook for 4 to 5 minutes, stirring almost constantly until the leaves are bright green and wilted.
Add the infused milk and cheese mixture and bring almost to the boil. Ladle into a blender and process to a thick but not totally smooth soup. Check the seasoning – you are likely to need black pepper but not salt.
To finish, cut the reserved sprouts in half and fry lightly in the butter. Toss them with the stilton and add to each bowl as you serve.