Bring the stock to a boil in a large pan. Add a large pinch of salt. Add broccoli and boil rapidly.
Whilst cooking the broccoli, roast the walnuts in a hot oven until golden brown all over. Take out and cool, break the walnuts into small pieces. Crush half the walnut pieces in a pestle and mortar until a rough sand texture and reserve the other half. Fold the crushed walnuts into the whipped cream and season with salt and pepper. Cover and chill until serving.
The broccoli is ready when you can pierce it with little or no effort. Remove the stock pan from the stove and reserve the stock. Use a slotted spoon to add broccoli to a blender but be careful because it’s boiling hot! Pour enough of the stock left over from cooking the broccoli to fill the blender halfway. Add a pinch or to taste of salt. Use several pulses on your blender to break the broccoli up and then puree for several seconds.
Pour soup into shallow bowl Spoon a big dollop of walnut Chantilly into each bowl along with the remaining walnuts.
Drizzle lightly with olive oil and serve at once.
The following types of blue cheese will work well in this recipe: stilton, roquefort, cambozola, cashel blue, danish blue cheese, dolcelatte and gorgonzola.