Heat oven to 375 degrees.
Brush mushroom caps with 1 tablespoon olive oil and sprinkle with salt and pepper. Place wire cooling rack on rimmed baking sheet, and then place mushroom caps top-side down on the rack. Spoon ¼ cup marinara into each mushroom cap. Top with mozzarella and cherry tomatoes. Add one slice of prosciutto to each mushroom. Bake for 20–25 minutes until mushrooms are softened and cheese is melted. While baking, toss arugula with remaining olive oil and parmesan.
Add freshly ground pepper if desired.