In a heavy stock pot, sauté the onion in 1 tablespoon melted butter. Whisk in butter and flour over medium heat for about 3-4 minutes.
Slowly whisk in the heavy cream and chicken stock. Let it simmer for about 20 minutes.
Add the broccoli, carrots, and onions. Let them simmer on medium low for about 25 minutes until the broccoli and carrots are tender.
Add nutmeg, salt and pepper and sharp cheddar cheese. Let the cheese melt and then serve.