In a pot over medium heat, add olive oil and onions. Cook for5 minutes or until onions are translucent. Add broccoli and cayenne pepper and cook for 3 minutes. Add stock and a little water so there is enough liquid to cover the vegetables.
Bring to a boil, cover and simmer on low for 30 minutes. Transfer soup to a blender and blend until smooth.
Return soup to pot and stir in milk.
Season with salt & pepper and top with basil. Serve.