Heat the butter in a large saucepan/dutch oven.
Add in the onion and saute for about 4 minutes, or until soft.
Sprinkle flour onto the onions and cook another 2-3 minutes, or until no more lumps appear.
Add in the milk and vegetable broth.
Bring to a rapid boil, then reduce heat and allow to simmer for about 15 minutes.
Add in the broccoli and carrots.
Cook about 15-20 minutes, or until vegetable are tender.
Add salt, pepper, hot sauce, and cheese and stir until cheese is melted.
Serve warm with crusty bread!!