Preheat oven to 400 degrees F. Line 2 baking sheets with foil; lightly coat the foil with cooking spray. Set baking sheets aside. For filling, in a medium bowl, stir together spinach, cream cheese, 2 tablespoons Parmesan cheese, green onion, and pepper. Set aside.
Unroll pizza dough on a lightly floured surface; roll dough into a 15-inch square. Using a pizza cutter or sharp knife, cut into twenty five 3-inch squares. Spoon a slightly rounded teaspoon of filling onto the center of each square. In a small mixing bowl use a fork to combine egg white and water. Brush edges of dough squares with egg white mixture. Lift a corner of each square and stretch dough over filling to opposite corner, making a triangle. Press edges with the tines of a fork to seal.
Arrange the calzones on prepared baking sheets. Prick tops of calzones with fork. Brush tops of calzones with egg white mixture. Sprinkle with remaining 1 tablespoon Parmesan cheese. Bake one sheet at a time for 8 to 10 minutes or until golden brown. Cool slightly on baking sheets. Serve warm.
Make Ahead Tip: The spinach filling may be made the day ahead. Cover and chill in refrigerator. Let stand at room temperature for 30 minutes to soften, if necessary.