Melt the butter and olive oil in a large pot over medium heat.
Add the sliced onions and sauté until soft, about 30 minutes, stirring occasionally.
Sprinkle in the sugar and continue cooking until the onions reach a deep brown color.
Deglaze the pot with white wine, scraping the bottom to release browned bits.
Add the beef broth, thyme, and bay leaf; bring to a simmer.
Simmer uncovered for about 30 minutes, allowing flavors to meld.
Preheat the broiler in your oven while the soup simmers.
Remove bay leaf and season the soup to taste before serving.
Ladle the hot soup into oven-safe bowls and top each with toasted baguette and cheese.
Broil the bowls for 3–5 minutes until the cheese is bubbly and golden brown.