Sauté onion in 1 tablespoon melted butter in large pot until soft.
Add flour and ¼ cup melted butter. Stir with onions over medium heat 3-4 minutes until thickened.
Slowly whisk in heavy cream and chicken broth.
Add broccoli and carrots. Simmer covered on medium-low for 25 minutes until vegetables are tender.
Add nutmeg, salt, pepper and cheddar cheese. Stir until cheese melts.
