Prepare the Broccoli: Break the broccoli into florets and roughly chop any tough stems. Reserve a couple of small florets for garnish.

Sauté Aromatics: Melt the butter in a large pan. Cook the chopped onion and leek until they soften, ensuring they don't caramelize.

Add Vegetables and Stock: Add the broccoli florets and diced potato to the pan. Pour in the chicken stock.

Simmer: Cover the pan and simmer for 15-20 minutes, or until the vegetables are tender.

Puree the Soup: Allow the soup to cool slightly. Use a blender, food processor, or immersion blender to puree the soup until smooth.

Add Dairy and Season: Return the pureed soup to the pan. Stir in the milk and double cream. Season with salt and black pepper to taste.

Reheat and Melt Cheese: Gently reheat the soup, ensuring it doesn't boil. At the last moment, add the crumbled Stilton cheese and stir until it just melts.

Prepare Garnish: Cut the reserved broccoli florets into thin slices.

Serve: Ladle the soup into warmed bowls. Garnish with the sliced broccoli and freshly ground black pepper. Serve immediately.