In a Dutch oven, heat 4 tablespoons oil over medium heat. Add onions; cook and stir until softened, 10-13 minutes. Reduce heat to medium-low; cook, stirring occasionally, until deep golden brown, 30-40 minutes. Add mushrooms, garlic, balsamic vinegar and soy sauce; cook 2 minutes longer.
Stir in wine. Bring to a boil; cook until liquid is reduced by half. Add broth, pepper and salt; return to a boil. Reduce heat. Simmer, covered, stirring occasionally, for 30 minutes. Uncover and let simmer for another 30 minutes.
Meanwhile, preheat oven to 400°. Place baguette slices on a baking sheet; brush both sides with remaining oil. Bake until toasted, 3-5 minutes on each side. Rub toasts with halved garlic.
To serve, place twelve 8-oz. broiler-safe bowls or ramekins on baking sheets; place 2 toasts in each. Ladle with soup; top with cheese. Broil 4 in. from heat until cheese is melted.
