In a large pot or Dutch oven, melt the butter and olive oil over medium heat.

Add the sliced onions to the pot and cook for 25 to 30 minutes, stirring frequently, until they become soft, sticky, and a deep golden brown color.

Stir in the minced garlic and cook for about 1 minute until fragrant, then sprinkle the flour over the onions and stir well to coat, cooking for another 2 minutes.

Pour in the dry red wine and balsamic vinegar to deglaze the pot, scraping up any browned bits stuck to the bottom with a wooden spoon.

Add the beef broth, fresh thyme, and bay leaf, then bring the mixture to a boil before reducing the heat to low.

Simmer the soup uncovered for 20 minutes to allow the flavors to meld together, then season with salt and black pepper to taste.

While the soup simmers, preheat your oven broiler and lightly toast the baguette slices on a baking sheet until crisp.

Remove the bay leaf, ladle the soup into oven-safe bowls, top with toasted bread, and cover generously with grated Gruyère cheese.

Place the bowls under the broiler for 3 to 5 minutes until the cheese is melted, bubbly, and slightly browned on top.