In a large saucepan, cook onions in butter over medium-low heat for 15-20 minutes or until tender and golden brown, stirring occasionally. Add beef and broth. Bring to a boil. Reduce heat; cover and simmer for 10 minutes.
In a small bowl, combine the flour, mustard and sugar; stir in wine or additional broth and browning sauce until smooth. Stir into soup. Bring to a boil; cook and stir for 1-2 minutes or until slightly thickened.