Preheat a grill, having one side prepared with indirect heat. Rub a tablespoon of olive oil on each side of the dough. Place the dough on the grill (not over the direct flame) and close the lid. Cook for a couple of minutes, then turn it over and close the lid. Transfer to a plate and set aside. Combine the remaining 4 tablespoons oil with the vinegar, salt, and pepper in a medium bowl and whisk together. Add the arugula, onion, tomatoes, prosciutto, and Asiago. Toss the salad in the dressing and transfer it to the cooked dough.