Broccoli-Mushroom Chowder

1 Pound fresh broccoli, cut into bite-size pieces
8 Ounces fresh mushrooms, coarsely chopped
8 Ounces butter
1 Cup flour, sifted
4 Cups chicken broth
4 Cups half & half
1 Teaspoon salt
1/4 Teaspoon white pepper
1/4 Teaspoon tarragon leaves, crushed

Steam broccoli in 1/2 cup of water until tender, do not drain. Set aside. Melt butter in saucepan over medium heat. Add flour to make a roux. Cook 2 to 4 minutes. Add chicken broth, stirring with a wire whip, bring to a boil. Turn heat to low. Add broccoli, mushrooms, half & half, and spices. Heat, but do not boil.