Caramelize the onions and mushrooms. Put 1 Tbsp olive oil in a medium saucepan. Add onions and mushrooms and cook on medium heat for about 10 minutes stirring frequently. If it starts to burn, turn the heat down. Add a dash of salt and 1 Tbsp brown sugar. Combine until sugar melts and cook 1 more minute. Remove from heat and set aside.
Place a pizza stone or baking sheet in the oven and preheat to 450 degrees F. Remove when heated and spray with cooking spray or lightly flour the surface. Roll out the dough on a lightly floured surface into a 12-inch round. Slide the dough onto the hot pizza stone or baking sheet. Bake 10 minutes.
Remove the pizza from the oven. Top your pizza with Parmesan cheese, mozzarella cheese, caramelized mushrooms and onions, and prosciutto slices. Drizzle with olive oil and a dash of salt and pepper. Return the pizza to the oven; bake until the cheese is golden and bubbly, about 6 more minutes.
Remove pizza from oven and top the pizza with arugula and 2 Tbsp shaved Parmesan. Cut into slices. (Optional) add a drizzle of glazed balsamic vinegar to slices.