Combine Parmesan cheese, paprika, salt and red pepper in small bowl.
On lightly floured surface with rolling pin, roll one pastry sheet into 18 x 8-inch rectangle. Brush surface with egg. Sprinkle with 1/2 cup cheese mixture; press mixture into sheet with rolling pin. Turn sheet over. Repeat with egg and cheese mixture. Starting from one 8-inch end, fold one-third of dough over middle one-third; fold opposite one-third over both to make 8 x 6-inch rectangle. Repeat with remaining sheet. Cut each sheet lengthwise into twelve 1/2-inch-wide strips.
Heat oven to 400 degrees F.
Place strips 1/2 inch apart on ungreased large baking sheets, twisting each strip twice and pressing ends onto sheet to prevent strips from uncurling during baking.
Bake in 400 degree F oven 12 to 15 minutes or until puffed and golden. Remove straws from baking sheets to wire racks to cool. Store in tightly covered container. Makes 2 dozen straws.