• Heat the beef stock in a large pot until it begins to simmer.
• Reduce the heat to its lowest setting, cover the pot with a lid to retain the warmth.

2. Caramelizing the Onions:

• In a heavy-bottomed pot, combine butter and vegetable oil, and heat over medium-low heat until the butter has melted.
• Add the sliced onions, ensuring they are evenly coated with the butter-oil mixture.
• Cover the pot and let the onions cook for about 15 minutes, stirring occasionally.
• Remove the lid, increase the heat slightly. Add salt, sugar, and flour. Stir consistently to ensure the onions don’t stick to the bottom and that the flour doesn’t burn. This process, which can take 35-40 minutes, is crucial for achieving that rich golden color and deep flavor in the soup.

3. Incorporating the Stock:

• Once the onions are properly caramelized, pour in the simmering beef stock and 1/2 cup of the white wine.
• Adjust the seasoning by adding salt, pepper, and an additional pinch of sugar if desired. Partially cover the pot and let it simmer for about 40 minutes.
• Use a spoon to remove any foam that might form on the surface.
• Stir in the remaining 1/4 cup of white wine. Adjust the seasoning if necessary. (Note: At this point, the soup can be cooled, covered, and refrigerated for up to three days. Simply reheat before continuing.)

4. Preparing the Toppings:

• Preheat the oven to 350°F.
• Generously brush both sides of each baguette slice with olive oil and place them on a rimmed baking sheet.
• Toast the slices in the oven for 4-5 minutes on each side or until crisp. Once done, set them aside.

5. Assembling the Soup:

• Arrange ovenproof bowls or ramekins on a baking sheet. Pour the hot soup into each bowl, filling them up to 3/4 full.
• Distribute the slivered Gruyère cheese among the bowls.
• Float 2-3 toasted baguette slices on the surface of each soup-filled bowl.
• Sprinkle a generous amount of the grated Gruyère cheese over the bread. (Note: Depending on the size of your bowls, you might have some leftover soup, cheese, or croutons.)

6. Baking the Soup:

• Bake the prepared soup in the oven until the cheese melts and turns light brown, approximately 15 minutes. Ensure you keep an eye on them so the cheese doesn’t burn.
• For a deeper brown color, you can place the bowls under a broiler for an additional 1-2 minutes. Ensure you watch them closely to avoid burning.

Serve immediately and enjoy the warm, comforting flavors of a French culinary classic!