Whisk the olive oil, vinegar, salt in a bowl. Add a generous grind of the black pepper.
Preheat oven to 475 degrees F. If you have a pizza stone, place it on the middle rack of the oven.
On a lightly floured surface, roll the dough quite thinly into a 13-inch round.
If you are using a pizza stone and peel, sprinkle the pizza peel generously with cornmeal. (see notes if you don’t have a stone or peel or if you have one and not the other)
Transfer the crust to the pizza peel. Generously brush with some of the balsamic dressing.
In a bowl, toss the onions with a tablespoon of so of the balsamic dressing, and then scatter the onions evenly over the dough, leaving a 1-inch border.
Sprinkle with about ¾ of the cheese.
Toss the arugula with the remaining balsamic dressing. Scatter on top of the onions and cheese. Arrange the peach slices over the arugula. Sprinkle with the remaining cheese. Give everything a generous grind of black pepper.
Gently jiggle the pizza peel to make sure the pizza will slide off easily. Tip the peel to the back of the preheated baking stone, and pull it away quickly, releasing the crust onto the stone. Bake until the crust is brown, 8 to 10 minutes on the stone. (see notes)
Remove the pizza stone from the oven, and place on a trivet or heatproof surface. Cut the pizza in wedges and serve. Alternatively, leave the pizza stone in the oven and slide the baked pizza back onto the peel or a rimless baking pan, then transfer to a serving platter.