Broccoli Cheese Soup

1/2 medium onion, chopped
5 T butter
1/4 cup flour
2 cups half and half (I use skim evaporated milk instead. )
2 cups chicken broth
8 oz chopped broccoli, fresh or frozen
1 cup shredded carrot
salt and pepper
2 cups grated sharp cheddar cheese
1/4 t ground nutmeg

Saute the onion in 1 T of butter. Set aside.
Using a wire wisk, combine 4 T of melted butter and flour over medium heat. Cook and stir for about 3 minutes.
Slowly add half and half, while stirring. Add the chicken broth and keep stirring. Simmer for 20 minutes.
Add the broccoli, carrots, and sauteed onion. Cook over low heat until veggies are tender, about 20 minutes.
Add salt and pepper
By now the soup should be thickened. Pour into blender or food processor and puree.
Return puree to low heat. Add the cheese and nutmeg and stir until blended.