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