French Onion Soup with Comté

Heat butter in a large heavy pot over medium-high heat. Add onions, shallots, and garlic; season with salt and pepper and cook, stirring occasionally, until softened and dark brown, 60–70 minutes. Add vermouth and vinegar. Bring to a boil, reduce heat, and simmer until slightly reduced, about 3 minutes.

Tie parsley, thyme, and bay leaf with kitchen twine; add to pot along with broth. Bring to a boil, reduce heat, and simmer, stirring occasionally, until reduced to about 8 cups, 35–40 minutes; discard herb bundle.

Preheat oven to 450°F. 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.