Melt butter in pot.
Add onions and cook a few minutes until fragrant.
Stir in flour and whisk well for a few minutes.
Add broth and cream and bring to a simmer.
Cook covered 25 minutes.
Add broccoli and carrots and simmer another 20 minutes.
Add salt/pepper generously to taste.
Add cheese and stir in until melted.
At this point, you can add more broth if you'd like to think it out.
Optional: puree soup if you want it smooth. I left it with the broccoli chunks.