1
Heat oil in a large, heavy stockpot on medium. Add onions and sprinkle with salt. Cook until softened and translucent, about 10 minutes.
2
Increase heat to medium-high and continue cooking, stirring often and scraping
3
The bottom of the pot, until onions are deep brown and caramelized, 40 to 50 min. If the bottom of the pot starts to get too dark, add 4 to 5 Tbsp water.
4
Sprinkle onions with flour and cognac and cook, stirring, about 2 more minutes. Add broth and herbs and simmer until reduced to about 8 cups, 18 to 20 min. Discard herbs and stir in vinegar.
5
When ready to serve, turn on your broiler. Place bread on a rimmed baking sheet and sprinkle with cheese. Broil on the top rack in the oven until cheese is golden brown and bubbling, about 2 minutes.
6
Ladle soup into bowls and top with cheesy toasts.