Preheat oven to 450°F. Coat two baking sheets with nonstick cooking spray. In a medium bowl combine the shredded chicken, cream cheese, hot sauce, ranch or blue cheese salad dressing, chopped green onions, and chopped celery.

Divide the dough into six portions; shape each portion into a ball. For each calzone, on a lightly floured surface roll one ball into a 7-inch circle. Spread about ½ cup chicken mixture on one half of the dough circle, leaving a 1-inch border. Top with about 2 Tbsp. pepper jack cheese. Lightly brush the edges with water. Fold the dough over filling; seal with the tines of a fork. Transfer the chicken calzones to a prepared baking sheet. Repeat with the remaining dough and fillings.

In a bowl whisk together the egg and 1 Tbsp. of water. Brush the tops of the calzones with egg mixture. Sprinkle with Parmesan cheese and Italian seasoning. Prick tops with fork or paring knife. Bake, rotating sheets once, until golden and hollow when tapped, 15 to 20 minutes. Cool slightly. Serve with additional ranch or blue cheese salad dressing.