Rinse the broccoli, cut off the florets from the stem and place them in a pot, the thick end of the stem can be discarded but tender parts of the stems also add to the soup. Cover broccoli with water and bring to a boil. Strain, pour in fresh water again and bring to a boil. Strain once more.
Pour hot broth or bouillon over the broccoli, salt if necessary and cook for about 1-2 minutes until the broccoli is al dente (be careful not to overcook as it will lose its green color).
Blend in a blender together with Gorgonzola cheese, basil leaves, a tablespoon of extra virgin oil, season with freshly ground black pepper.