adapted from Julia Child's French Onion Soup in The Way To Cook
Melt the butter and oil in a large dutch oven or stockpot set over medium heat. Add the sliced onions, stir them around, cover the pan, and cook slowly until tender, about 10 minutes.
Remove the lid from the onion pot, increate heat to medium-high, sprinkle in the sugar, and cook the onions until medium brown in color and caramelized, stirring frequently, about 45 minutes.
Sprinkle the flour over the onions and stir for 3 or 4 minutes. Remove pot from heat and stir in 2 cups of hot stock. Return pot to heat and bring to boil. Add remaining stock and vermouth. Cover loosely and simmer very slowly for 90 minutes, adding a little water if the liquid reduces too much.
To gratinée serving bowls: Preheat oven to broiling; position rack about 6 inches from heat. Pour a teaspoon or two of Cognac into each serving bowl. Ladle in the soup, about two-thirds full, and set on a rimmed sheet pan. Float a slice of toasted bread in each bowl (perhaps 2 baguette slices will fit) and sprinkle with grated cheese. Broil a few minutes until cheese is bubbly and starting to brown. (Alternatively, bake in 375° oven until cheese is melted, remove from oven, and brown the cheese using a hand-held butane torch.)