Measure the chicken broth into a large soup pot. Bring to a boil. Add the beans, turnips, leeks, carrots and barley; simmer over medium heat for 30 minutes. Add the Brussels sprouts and green pepper. Season with salt and pepper. Simmer until the sprouts are tender, about 30 minutes more.
Melt the butter in a small saucepan over medium heat, stirring until it starts to brown. Whisk in the flour until smooth. Stir this into the soup and simmer until thickened, about 10 minutes.
