1Melt the butter and sauté the onions until soft. Sprinkle the flour over the mixture and cook for 1-2 minutes.
2Whisk in the half-and-half and chicken stock. Bring to a boil, then reduce heat to medium.
3Add broccoli and carrots. Cook over medium-low heat for 20-25 minutes, or until the vegetables are tender.
4Add salt and pepper. Blend about 1 cup of the soup for a smoother consistency, if desired. Return to low heat, add cheese, and stir in nutmeg (optional).