- In a large pot over medium heat, melt the butter and olive oil. 
- Add the garlic and cook for 1-2 minutes, or until fragrant. 
- Add the chopped broccoli, chicken or vegetable broth, heavy cream, cheddar cheese, Parmigiano Reggiano, salt and pepper to the pot. 
- Bring to a boil, then reduce the heat and simmer for 20-25 minutes, or until the broccoli is tender. 
- Use an immersion blender or transfer the soup to a blender and blend until smooth. 
- Taste and adjust seasoning as needed. 
- Serve the soup warm, garnish with additional cheese and/or chopped herbs, if desired.