Making Broccoli Cheddar Soup is straightforward. Just follow these steps:

1. Prepare the Vegetables: Wash and cut the broccoli into small florets, dice the onion, and mince the garlic.
2. Sauté the Onion and Garlic: In a large pot, heat the olive oil over medium heat. Add the diced onion and cook until softened, about 5 minutes. Stir in the minced garlic and cook for an additional 1-2 minutes until fragrant.
3. Add Broccoli and Broth: Add the broccoli florets to the pot, followed by the vegetable broth. Bring the mixture to a boil.
4. Simmer: Reduce heat to low and let the soup simmer for about 15 minutes, or until the broccoli is tender.
5. Blend the Soup: Remove the pot from heat. Using an immersion blender, carefully blend the soup until smooth. If you prefer a chunkier texture, you can blend only half of it and leave some broccoli pieces intact.
6. Add Cream and Cheese: Return the pot to low heat. Stir in the heavy cream, shredded cheddar cheese, salt, black pepper, and cayenne pepper (if using). Continue stirring until the cheese has completely melted.
7. Season to Taste: Taste the soup and adjust seasoning if needed. You can add the optional Dijon mustard for an extra layer of flavor at this stage.
8. Serve Hot: Ladle the soup into bowls and, if desired, top with a sprinkle of additional cheese or fresh herbs.