In the same large pot, melt ¼ cup butter over medium heat. Add flour and stir to combine. Continue to stir until butter mixture has thickened, about 3 minutes. Whisk in half and half and broth and simmer for 20 minutes.
Add broccoli, carrots and onions. Simmer for another 25 minutes, or until broccoli and carrots are tender. Add nutmeg, cheese and salt and pepper, to taste. Stir until cheese has completely melted into the soup.
Serve hot.
Recipe by The Little Chef at http://littlechefblog.com/panera-broccoli-cheddar-soup/