- 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.
- With the rack in the middle position, preheat the oven’s broiler.
- Ladle the soup into four ovenproof bowls. Place a slice of bread onto each soup and sprinkle with the cheese. Place the bowls on a baking sheet and broil in the oven until the cheese has melted.