In a skillet heat olive oil over medium heat. Add diced garlic and saute for 1 minute. Add chopped mushrooms and saute for 4-5 minutes. Add balsamic vinegar, salt and black pepper; increase heat to medium-high and cook uncovered, stirring until all the liquid is absorbed.
Preheat oven to 375 degrees F. Arrange slices of bread on a baking sheet. Place half a slice of cheddar cheese on top of each bread. Place the mushroom mixture on top of the cheese and sprinkle with dried oregano.
Bake in the oven until cheese is melted, about 6 minutes. Serve warm.