Preheat oven to 450 degrees with rack in lower third. Toss together asparagus, onion, and 1 tablespoon oil in a medium bowl. Season with salt and pepper.
Brush a rimmed baking sheet with 2 tablespoons oil. Using your hands, gently stretch dough from all sides to approximate size of baking sheet. Place dough on baking sheet, stretching and fitting it to edges of sheet.
Brush dough with remaining 2 tablespoons oil, then spread with ricotta, leaving a 1/2-inch border. Top with asparagus mixture; sprinkle with mozzarella.
Bake until crust is golden brown and asparagus is tender, about 20 minutes. Top with watercress, season with salt, and sprinkle with pepper flakes. Cut into pieces and serve.