Pat hot dogs dry. Preheat oven to 400ºF. On a lightly floured surface, unfold thawed puff pastry sheet. Press fold perforations together to make a solid sheet. Using a rolling pen, roll pastry sheet to measure 15 by 10 inches. Cut into 10 rectangles, each measuring 3 by 5 inches. Roll each hot dog in pastry rectangle, gently stretching and pressing dough ends together to seal. Cut each wrapped hot dog into 3 pieces (about 1 1/2 inches). Beat egg and water together in a small bowl. Quickly dip each wrapped hot dog into egg wash and then roll in cheese, coating all surfaces. Place, 1 inch apart, seams side down, on baking sheets lined with parchment paper or sprayed with nonstick cooking spray. Bake in preheated 400ºF oven for 15 minutes or until pastry is light brown. Immediately transfer to cooling rack. Serve warm with assorted mustards or barbecue sauces.