Preheat oven to 475 degrees F. Line a large baking sheet with parchment paper; set aside. In a large bowl combine mushrooms; asparagus, beans, zucchini, and or snap peas; sweet peppers; onions; oil; and salt. Spoon vegetable mixture onto the prepared baking sheet, spreading evenly. Roast for 10 minutes; remove from oven and set aside.
Place flatbreads on two large baking sheets; sprinkle with Pecorino-Romano cheese. Top with roasted vegetables and cherry tomatoes; sprinkle with mozzarella cheese. Roast about 5 minutes more or until mozzarella cheese is melted.