Heat 1 tablespoon butter in a large pot over medium heat. Add onion along with a large pinch of salt and pepper and cook for 3-4 minutes, stirring frequently. Add garlic and cook for an additional minute.
Turn heat to medium low and melt remaining 6 tablespoons butter in the pot with the onion and garlic.
Add flour and stir to combine. Cook for about 1 minute, stirring frequently.
Add veggie broth and milk.
Then add ground mustard, cayenne pepper and a pinch of salt and pepper. Stir to combine.
Next stir in both cheeses until they are completely melted.
Add broccoli, cover pot and simmer over medium low heat for 20 minutes, stirring every 5 minutes.
If the soup seems to be simmering too rapidly or almost boiling, turn the heat down a bit. You want a gentle simmer for 20 minutes.
You’ll know the soup is done when the broccoli is tender.
Serve with shredded cheese and a couple slices of crostini and enjoy!
To make the crostini: Slice French bread into 1/2″ thick slices and lay on a baking sheet. Drizzle with olive oil and broil for 1-2 minutes or until golden brown. Flip bread over and broil the other side for 1-2 minutes or until golden brown. Serve with soup and enjoy!