In a large pot over medium heat, simmer the broccoli in the broth for 15 minutes. In a separate skillet over medium heat, melt the butter, or margarine, add onions and sauté for 5 minutes, or to desired tenderness. Add the flour to the onions and stir well, forming a pasty substance. Gradually add the milk and stir until thick add this mixture to the broccoli mixture in the pot and stir well. Then add the cheese, stirring until melted finally add the pepper( be careful not to let the soup boil, or the cheese will break down.)