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