Position oven rack 6 inches from broiler heat source; heat broiler on high. Heat 2 tablespoon oil in large skillet on medium-high.
Add mushrooms, thyme and mint and cook, stirring occasionally, until mushrooms give off juices and begin to brown, about 6 minutes. Add shallot and garlic and cook, stirring occasionally, until tender, about 2 minutes.
Stir in wine and simmer until almost completely reduced, about 2 minutes. Season to taste with salt and pepper. Remove from heat; keep warm.
On broiler-safe baking sheet, drizzle bread with about 1 tablespoon oil. Toast bread in broiler 1 minute; turn and lightly toast other side, about 30 seconds. Divide fontina evenly over bread; broil until cheese is melted and crust is browned, about 1 minute.
Remove and discard herb sprigs from mushroom mixture. Transfer bread to cutting board; top with mushroom mixture. Cut each slice in half vertically to make 8 pieces; top with fresh thyme sprig, if desired. Serve immediately.