Preheat oven to 400°F and place rack in the top position.
Place pizza crust on a baking sheet or pizza stone and spread pesto over the crust generously. Top with the tomatoes and mozzarella and crushed red pepper, if using.
Bake on the top rack at 400°F until slightly crispy (about 6 minutes). Then, turn the broiler to high, and broil another 1-2 minutes. Remove from the oven and let cool while you assemble the salad.
In a medium bowl, whisk together vinegar, oil, 1/4 teaspoon salt, and black pepper. Add the arugula and toss to combine. Arrange salad evenly over pizza, topping with the sliced red onion and parmesan. Cut into 8 slices and serve immediately.