In a large heavy pan, soften the onions in the butter, then add the potato and broccoli and cook for a couple minutes.
Next add the stock, cover, and simmer for about 20-25 minutes. Allow to cool down for about 15-20 minutes and then blend the mixture until smooth.
Gently reheat, and add the cream and Stilton, stirring until all the cheese has melted. Add a decent amount of black pepper and serve immediately.