In a large non-stick saucepan over medium-low heat, cook the onions in the butter until lightly browned and tender, about 30 minutes. Season with salt and pepper. Sprinkle with the flour and cook for 1 minute. Add the beer and mustard and bring to a boil while stirring. Add the broth and bring to a boil, then simmer for 10 minutes. Add more chicken broth, if needed. Adjust the seasoning.
