Place the slices of bread on a baking sheet, Use 2 tablespoons of olive oil to brush on one side of the slices.. Place them under the broiler for 1-2 minutes until they are golden. Set aside. Turn off the oven.
Heat 2 tablespoons of the olive oil in a skillet over medium heat. Add the onion slices and cook until they are soft and a deep brown, about 25 to 30 minutes, Transfer to a dish and reserve.
In the same skillet set over medium heat add the mushroom slices. Cover and cook, stirring occasionally for 8-10 minutes until the mushrooms have released their liquid. Remove the lid, add the remaining 2 tablespoons of oil and cook until the mushrooms are a golden brown. Add the garlic, fresh thyme and salt. cook for another 30 seconds until the garlic is soft and fragrant. Transfer to a dish and set aside.
Turn on the oven broiler again:
With the toasted bread on the baking sheet, add a portion of the cheese to each bread slice, transfer to the oven and allow the cheese to melt slightly. Remove the baking sheet from the oven and assemble the bruschetta.
Divide the onion and mushrooms over each of the slices of bread, and garnish with fresh herbs. Transfer the bruschetta to a platter and serve warm or at room temperature
Notes
The topping can be prepared 1-2 days in advance, stored in the refrigerator and re-warmed before serving.
Options for a good melting cheese: Monterey Jack, Havarti, Provolone, Munster, Smoked Gouda