To prepare soup, heat oil in a large pot over medium-high heat. Add onion to pan; saute 15 minutes or until almost tender, stirring frequently. Reduce heat to medium-low; cook until deep golden brown (about 40 minutes), stirring occasionally.
Increase heat to medium. Add mushrooms to pan; cook 10 minutes or until mushrooms are tender (less is using canned mushrooms), stirring frequently. Stir in garlic and thyme; cook 2 minutes, stirring frequently. Increase heat to medium-high. Add wine to pan; cook 2 minutes or until most of the liquid evaporates. Add broths to pan; bring to a simmer. Reduce heat, and simmer 45 minutes (we've done it for less time). Stir in salt and pepper.
To prepare toasts, preheat broiler. Arrange bread in a single layer on a baking sheet. Top each bread slice with 1 tsp cheese. Broil 2 minutes or until cheese melts. Sprinkle thyme over cheese.
Ladle about 1 cup soup into each of 6 bowls; top each serving with 2 toasts.