Bring broth and 1 can water to a boil in a large pot. Stir cheese, broccoli, carrots, potatoes, and onion into the boiling liquid; cook, stirring frequently, until the cheese is completely melted and the mixture is smooth, about 10 minutes.
Season the soup with salt and black pepper. Pour beer into the soup, bring to a boil, and cook until the liquid is slightly reduced, about 5 minutes.
Whisk cornstarch and 1 tablespoon water together in a small bowl; pour into the soup and stir. Cook until the soup thickens, about 5 minutes.