In a large pot over medium high heat melt the butter. Add the onions, brown sugar and salt, allow to simmer over low to medium heat, stirring occasionally, until onions are a dark golden brown, at least 30 minutes and up to one hour (the longer onions cook the more flavor develops).
Add ½ cup stout beer, simmer until the beer is reduced and the pan is almost dry.
Add the remaining beer, beef stock and black pepper. Simmer for ten minutes.
Pre heat the broiler on your oven.
Ladle soup into bowls, top with slices of French bread toast and then cheese.
Broil until the cheese has melted.