In a large pot, melt the butter with the olive oil over medium heat. Add the onions and cook, stirring frequently, until the onions are golden brown and caramelized, about 25 minutes.
Stir in the beef and chicken broths, white wine, Worcestershire sauce, thyme, and black pepper. Bring the mixture to a boil, then reduce the heat and let it simmer for 20 minutes.
Preheat the broiler. Ladle the soup into oven-safe bowls, and place a slice of toasted bread on top of each serving.
Divide the grated Gruyère cheese among the bowls, covering the bread. Broil until the cheese is bubbly and golden brown, about 3 minutes.
Serve hot and enjoy your Outback Steakhouse-Inspired Walkabout Onion Soup.
Notes
For a variation, you can substitute Gruyère cheese with Swiss cheese or another melting cheese of your choice.