Heat oil in a Dutch oven over medium-high heat. Add the onions; sauté for about 10 minutes or until tender. Reduce heat to medium-low. Stir in thyme, salt, and pepper and cook for about 40 minutes or until golden-brown, stirring occasionally.
Increase heat to medium-high. Add vermouth, scraping pan to loosen browned bits. Cook until liquid almost evaporates. Stir in stocks; bring to a simmer. Stir in soy sauce and cook for about 4 to 5 minutes. Taste and season with salt and pepper if needed.
Preheat broiler to high with rack in top position. Ladle soup into 6 broiler-safe soup bowls. Top each serving with 2 bread slices, and sprinkle evenly with cheese. Place soup bowls on baking sheet and broil for about 3 or 4 minutes or until tops are golden brown and cheese bubbles. Enjoy!