Step 1

Preheat the oven to 375 degrees F.

Step 2

Roll out each sheet of puff pastry on a lightly floured board until it's 10 by 12 inches. Beat the egg with 1 tablespoon of water and brush the surface of the pastry. Sprinkle each sheet evenly with 1/4 cup of the parmesan, 1/2 cup 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.

Step 3

Bake for 10 to 15 minutes, until lightly browned and puffed. Turn each straw and bake for another 2 minutes. Don't overbake or the cheese will burn. Cool and serve at room temperature.

Step 4

Let the puff pastry thaw in the refrigerator overnight.