Saute onion, carrots, celery, and butter in a large pot over medium heat.
Stir and cook until translucent.
Stir again.
Add flour, and stir.
Pour in broth, and add spices.
Add broccoli
Let it simmer over medium-low heat for about ten minutes before adding the cheese and cream.
Let it simmer for another ten minutes.
Add salt and pepper to taste. Bon Appetit!