In a large pot, I melt the butter and olive oil over medium heat. Adding the thinly sliced onions, I cook them until they've softened and turned translucent, which takes about 18 to 20 minutes. To enhance their sweetness, I sprinkle in salt, pepper, and sugar, then continue cooking for another 30 minutes, stirring constantly, until the onions achieve a deep golden hue.

Turning up the heat to high, I pour in the white wine. I let it cook for about 12 minutes, allowing the wine to reduce almost entirely, which concentrates its flavors.

Next, I add the beef broth, dried thyme, and rosemary to the pot. Bringing the mixture to a gentle simmer, I let it cook for approximately 20 minutes, stirring occasionally, until the flavors meld beautifully.

While the soup simmers, I preheat my oven's broiler. I arrange the toasted baguette slices on a baking sheet and sprinkle them generously with the shredded cheese. Placing them under the broiler, I watch closely until the cheese melts and turns bubbly, which usually takes just a few minutes.

Ladling the hot soup into oven-safe bowls, I top each with the cheesy bread. For an extra touch, I sometimes garnish with fresh herbs and a crack of black pepper before serving immediately.