Split onions and slice. In large Dutch oven over medium heat, melt butter. Add onions, sugar, and a pinch of salt. Cover and cook over low heat, stirring occasionally, until onions are tender but not colored, about 30 minutes. Uncover pan, increase heat and continue to cook, stirring regularly until onions are rich caramel color (10 to 15 minutes). Do not let onions burn!
Sprinkle in flour and stir until well blended. Stirring constantly, gradually add wine and bring to a boil. Stir in beef broth and pepper; bring to boil. Reduce heat to low. Cover and simmer 15 minutes, taste and adjust. (Not too much salt, cheese is also salty.)
Ladle soup into oven proof bowls. Top each with bread slice; sprinkle with Swiss cheese, then Parmigiano-Reggiano, then paprika. Place bowls on baking pan. Broil until cheese melts and begins to brown – don’t walk away, it may burn!
