Preheat oven to 475°F (245°C) with a pizza stone or baking sheet inside.
Roll or stretch the pizza dough on a floured surface into a 12-inch circle.
Spread the pizza sauce evenly over the dough, leaving a 1-inch border for the crust.
Distribute the fresh mozzarella slices and dried oregano over the sauce.
Transfer the pizza to the preheated oven and bake for 10 to 12 minutes until the crust is golden brown and the cheese is bubbling.
While the pizza bakes, toss the arugula and halved cherry tomatoes in a bowl with olive oil, salt, and pepper.
Remove the pizza from the oven and allow to rest for 2 minutes.
Distribute the arugula and tomato mixture evenly over the hot pizza.
Top with shaved parmesan cheese and drizzle with balsamic glaze before slicing and serving.