1. Position oven rack in the lowest position; preheat to 450°F. Coat a large baking sheet with cooking spray.
2. Roll out dough on a lightly floured surface to about the size of the baking sheet. Transfer to the baking sheet. Bake until puffed and lightly crisped on the bottom, 8 to 10 minutes.
3. Meanwhile, 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.
4. Spread pesto evenly over the crust, top with the broccoli mixture and sprinkle with cheese. Bake until crispy and golden and the cheese is melted, 8 to 10 minutes.