Remove pizza dough from fridge. Place 1 tablespoon of olive oil in a medium bowl. Add pizza dough to bowl and toss in oil. Let it sit at room temperature for 1 hour to warm up. As the dough warms up, it will grow, which is good.
Preheat oven to 450 degrees. Slice fresh mozzarella in slices and halve the tomatoes. Set aside.
Punch dough down with your fist to remove air bubbles. Place pizza dough on a large baking sheet and spread with your fingers until dough is 1/4 inch thick, leaving a slight lip around the edges for the crust. Place sliced mozzarella and tomato halves evenly all over the dough. Sprinkle with a little bit of sea salt.
Bake pizza in preheated oven for 15 minutes, or until cheese is bubbling and crust turns slightly golden brown. Place prosciutto and arugula on top of the hot pizza. Let it cool for 2 minutes. Slice into 8 even slices and then serve.