ROLL out each ball of pizza dough on lightly floured surface into 12x7-inch oval, 1/8 inch thick. Grill on medium-high heat 2 to 3 min. or until grill marked on both sides. Remove from grill. Brush both sides of each crust evenly with 1 tsp. of the dressing; set aside.
SAUTE onions in remaining dressing in large skillet on medium-high heat 1 to 2 min. or until onions are translucent. Place in large bowl. Add asparagus and tomatoes; mix lightly.
FOR each serving: Place 1 flatbread in parchment paper-lined sheet pan. Top with 1-1/2 oz. ham, about 3/4 cup of the vegetable mixture, 3/4 cup of the mozzarella cheese and 2 Tbsp. each of the Parmesan and Asiago cheeses. Bake in 375ºF-convection oven 4 to 5 min. or until cheese is melted. Sprinkle with 1 Tbsp. basil.