Sauté onion in 2 tablespoon of butter, set aside.

Cook 1/2 cup melted butter and flour using a whisk for about 5 minutes over medium heat stirring constantly.

Slowly stir in half & half, and then add chicken stock, let simmer for about 20-25 minutes.

Add the sautéed onions, broccoli and carrots. Let cook for about 25-30 minutes.

Add salt & pepper and purée. Return to heat and slowly stir in cheese, then nutmeg.