- Cut the onions into wedges, then thinly slice widthwise to get short strips.
- In a large pot over medium heat, soften the onions in the butter for 15 minutes, stirring occasionally. Continue cooking over high heat for 15 minutes or until the onions are caramelized, stirring constantly and scraping the bottom of the pot. Deglaze with the wine and cognac. Let reduce until almost dry. Add the chicken and beef broths, the toasted flour and nutmeg. Mix well.
- Bring to a boil. Simmer over medium-high heat for 30 minutes or until the soup has reduced by half. You will have about 5 cups (1.25 litre) of soup. Season with salt and pepper.
- With the rack in the middle position, preheat the oven to broil. Place 4 ovenproof bowls on a baking sheet.
- Meanwhile, lightly rub each slice of bread with garlic. Divide the soup among the bowls and top each one with 2 tbsp of the cheese.
- Place 3 slices of bread over each bowl and top with the remaining cheese.
- Broil for 5 minutes or until the cheese is golden and melted.