Melt the butter in a large pot over medium heat. Add the onions, garlic. Meanwhile tie together bay leaves, thyme and rosemary with butchers twine.
Add to pot and season with salt and pepper. Cook until the onions are very soft and caramelized, about 25 minutes.
Add the vermouth, and red wine vinegar bring to a boil, reduce the heat and simmer until the vermouth has evaporated and the onions are dry, about 5 minutes.
Now add the beef broth, bring the soup back to a simmer, and reduce for 15 minutes. Season to taste with salt and pepper.
Preheat oven to 450°. Place ovenproof bowls on a large rimmed baking sheet.
Divide soup among bowls and top with toasts (cut to fit if necessary) and cheese. Bake until cheese is bubbling and golden brown, 6-8 minutes.
