In a large Dutch oven or soup pot, melt the butter over medium heat. Add the vegetable oil, onions, salt, pepper, and sugar. Cook uncovered, stirring occasionally, until the onions become deeply golden brown and caramelized. This process takes approximately 45–55 minutes. Stir frequently toward the end to prevent burning, and scrape any browned bits from the bottom of the pot.

Increase the heat to high and pour in the white wine. Cook while stirring continuously until the liquid is almost completely evaporated, leaving the onions with a jam-like consistency. This step should take about 8–10 minutes.

Sprinkle the flour over the onions and stir well. Cook for 1 minute, ensuring no lumps form. Add the beef broth, Worcestershire sauce, thyme, and bay leaves. Bring the mixture to a boil, then reduce the heat and let it simmer, covered, for 30 minutes.

While the soup simmers, preheat the oven to 400°F (204°C). Arrange the baguette slices on a baking sheet in a single layer and bake for approximately 10 minutes or until they are dry, crisp, and golden at the edges.

Remove the bay leaves from the soup. Stir in the dry sherry and adjust the seasoning with additional salt, Worcestershire sauce, or a pinch of sugar if needed.

Position an oven rack 6 inches from the broiler and preheat the broiler. Ladle the hot soup into oven-safe bowls placed on a baking sheet. Add one or two baguette slices to each bowl and generously sprinkle the Gruyère and Parmigiano Reggiano cheeses over the top. Broil for 3–5 minutes, or until the cheese is melted and bubbling around the edges.

Allow the soup to cool slightly before serving. If using regular soup bowls, broil the cheese-topped baguette slices separately and place them on top of the soup when serving.