01 - In a large, heavy-bottomed pot, melt the butter with the olive oil over medium heat.
02 - Add the sliced onions and a pinch of sugar. Cook, stirring frequently, for 30–40 minutes, until onions are deeply golden and caramelized. Reduce the heat if onions begin to burn.
03 - Stir in the minced garlic and cook for 1 minute.
04 - Pour in the white wine to deglaze, scraping the bottom of the pot to release any browned bits. Let simmer until wine is mostly evaporated, about 3–4 minutes.
05 - Add the broth, thyme, bay leaf, Worcestershire sauce, and brandy if using. Bring to a boil, then reduce heat and simmer uncovered for 25–30 minutes. Season to taste with salt and pepper. Remove the bay leaf.
06 - Preheat the oven broiler.
07 - Arrange bread slices on a baking sheet and toast under the broiler until golden on both sides.
08 - Ladle the hot soup into oven-safe bowls. Top each with a toasted bread slice and a generous mound of grated cheese.
09 - Place the bowls on a baking tray and broil until the cheese is bubbling and lightly browned, 2–4 minutes.
10 - Serve immediately, garnished with extra thyme if desired.