2) Roll out each sheet of puff pastry on a lightly floured board until it is 25x30cm. Beat the egg with 1 tbsp. of water and brush the surface of the pastry. Sprinkle each sheet evenly with half of the Parmesan, half of the Gruyere, 1/2 teaspoon of the thyme, 1/2 teaspoon of the salt, and some pepper. With the rolling pin, lightly press the flavorings into the puff pastry. Cut each sheet crosswise with a floured knife or pizza wheel into 11 or 12 strips. Twist each strip and lay on baking sheets lined with parchment paper. At this point you can transfer to a freezer-safe container to cook from frozen later. Please note, cooking times will increase when cooking from frozen and you may need to lower your oven temperature slightly.
3) Bake for 10 to 15 minutes, or until lightly browned and puffed. Turn each straw and bake for another 2 minutes. Don't over bake or the cheese will burn. Cool and serve at room temperature.