In a medium bowl, combine the Roma tomatoes, sherry vinegar, capers, sugar, crushed red pepper, salt, and basil; set aside.
In a medium nonstick skillet, melt the butter over medium heat.
Add the sliced cremini mushrooms, sliced shiitake mushrooms, and sliced baby portobello mushrooms; cook 5 minutes or until tender, stirring frequently.
Add the chopped green onions and minced garlic; cook for another 2 to 3 minutes until softened and fragrant.
Transfer the mushroom mixture to the bowl with the tomato mixture; toss well to combine.
Preheat your oven to 375°F (190°C) and arrange the toasted baguette slices on a baking sheet.
Spoon about 1 tablespoon of the mushroom and tomato mixture onto each slice of toasted baguette.
Evenly sprinkle the shaved Parmigiano-Reggiano over each bruschetta.
Place in the oven and bake for about 5 minutes until the cheese melts.
Remove from the oven, let cool slightly, and serve immediately.
