To prepare soup, heat oil in a large Dutch oven over medium-high heat.
Add onion to pan; saut 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, stirring frequently. Stir in garlic and thyme sprigs; 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. Stir in salt and pepper. Discard thyme sprigs.
To prepare toasts, preheat broiler.
Arrange bread in a single layer on a baking sheet. Top each bread slice with 1 teaspoon Gruyre and 1 teaspoon Gorgonzola. Broil 2 minutes or until cheese melts.
Sprinkle chopped thyme over cheese. Ladle about 1 cup soup into each of 6 bowls; top each serving with 2 toasts.