In a soup pot or high-sided pan over medium heat, combine the vegetable broth and crushed red pepper.
Allow the broth to warm to medium hot, then add the onion and garlic. Stir occasionally while the broth and vegetables continues to warm.
Add the chopped broccoli to the broth, then cover the soup pot and allow the broth and vegetables to simmer for 10 minutes.
Pour the soup into a blender and blend the soup until smooth.
Return the soup to the pot and heat over medium, adding the black pepper and additional crushed red pepper to taste. Once hot, remove the soup and serve.