Roll out dough on a lightly floured surface to about the size of the pizza pan. Transfer to the pan.
Cook broccoli and water in a large skillet over medium heat, covered, until the broccoli is crisp-tender, about 3 minutes. Stir in arugula and cook, stirring, until wilted, 1 to 2 minutes more. Season with salt and pepper.
Spread pesto evenly over the crust, top with the broccoli mixture, and sprinkle with cheese.