I'm a TOTAL spazz with pizza dough. I have all the equipment (stone! peel!). But the only trick that makes the process work for me consistently is to place the stretched dough onto a piece of parchment paper just slightly larger than the pizza and to slide the whole thing from peel to stone. Don't use too much extra parchment or it could scorch, but this discovery has saved me countless heartache, and I highly recommend it.
Place a pizza stone (or, in a pinch, an upside-down baking sheet) on a rack in the center of the oven. Preheat oven to 500°F.
Divide the pizza dough into two portions and stretch each into a 12-inch round. If you like, place each on a sheet of parchment just slightly larger than the dough. Top each dough round with 1/2 cup tomato sauce and spread well. Sprinkle each with half the mozzarella. Bake for about 10 minutes, until browned and bubbly. (I bake one at a time -- the first right before we're ready to eat and the second while we eat the first.)
Meanwhile, toss the arugula with the olive oil, lemon juice, flaky salt and plenty of freshly ground black pepper.
When each pizza is done, tear the prosciutto slices in half and arrange on top of pizza. Heap arugula salad in the center, then shower with curls of Parmigiano cheese. Top with more black pepper if you like, and drizzle with balsamic glaze. Cut into slices and serve immediately.