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.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.