Line a baking sheet with parchment paper. Unfold pastry on a lightly floured surface; brush lightly with some of the egg white. Sprinkle lightly with half of the pepper. Sprinkle with half of the cheese. Top with second sheet of puff pastry. Brush with egg white and sprinkle with remaining pepper and cheese. With a rolling pin, roll puff pastry to seal the sheets together and press cheese into the pastry, making a few passes.
Preheat oven to 375 degrees. With a pizza wheel, cut the pastry into long 1/2-inch strips. Gently twist each strip several times. Transfer to prepared baking sheet, pressing down ends. Bake for 18 to 20 minutes or until golden brown. Transfer to a wire rack and cool. Makes about 20 straws.