Heat oven to 500 degrees F. Lightly oil 2 (14-inch) pizza pans; set aside.
Divide pizza dough in half. Cover 1/2 with plastic wrap while working with the second. Working on a lightly floured surface, use fingers to flatten and stretch half the dough into a rough 8-inch circle. Transfer to 1 of the prepared pizza pans. Continue to press dough out until it fits just inside rim of pan. Dough should be less than 1/4-inch thick. Drizzle with olive oil. Repeat with second piece of dough.
Sprinkle each pizza with half the mozzarella. Transfer both to oven and bake until golden and crusty, 20 to 25 minutes. Remove from oven and top with prosciutto and arugula. Drizzle with olive oil. Serve immediately.
Measure the flour onto a clean work surface and make a well in the center. Dissolve the yeast in a bowl with 3/4 cup lukewarm water. Place the salt, yeast and olive oil in the well, and with the help of a fork, incorporate the flour into them. Add more lukewarm water as needed to make a dough that is homogenous and elastic.
Dust a large bowl with flour. Place the dough in the bowl. Cover with plastic wrap and set it in a warm place to rise until doubled in size, about 2 hours.
Oil 2 (12-inch) pizza pans each with 2 tablespoons. On a lightly floured surface, knead dough until very smooth. Divide dough in half. Using a rolling pin, roll each half, 1 at a time. Transfer dough to prepared pans. Stretch dough with your hands to form rounds 1/4-inch thick.