Move oven rack to lowest position. Place pizza stone on rack and heat oven to 500°F for one hour.

Divide pizza dough in half. Work with one piece at a time while the other piece remains covered. Place dough on a large piece of parchment paper. Cover with an 18" length of plastic wrap and let rest for 10 minutes.

Roll dough (while still covered with plastic) as thin as possible. Remove plastic wrap. Brush dough with 1 tsp olive oil. Arrange half of the tomato slices on the pizza dough. Season with freshly cracked black pepper and salt to taste. Bake until tomato slices have softened and crust is partially cooked, about 5 minutes.

Arrange half of the mozzarella on top of the tomato slices. Top with half of the prosciutto slices. Place pizza back in the oven until cheese is melted and crust is golden brown, about 5 more minutes.

While pizza is cooking, toss the arugula with 2 tsp olive oil and salt and pepper to taste. Spread half of the oiled arugula on top of the cooked pizza. Return pizza to oven until arugula just begins to wilt, 1-2 minutes. Allow pizza to cool for 5 minutes before cutting. Repeat with remaining ingredients.