In large skillet, heat oil over medium-high heat. Add onion; saute 1 minute. Add all mushrooms, garlic and thyme; saute until beginning to brown, about 6 minutes or until liquid evaporates. Remove from heat. Stir in cream and cheeses. Season with salt and pepper.
Top each toast with about 1 tablespoon mushroom topping. Place toasts on rimmed baking sheets. Working in batches, broil until cheese is melted and begins to brown, watching closely to prevent burning, about 2 minutes. Transfer to serving platter and serve warm.