Defrost the puff pastry according to the package directions. On a lightly floured surface, roll out the dough until it is about 1/16 inch thick. The size of the pastry will depend on the brand you use, but you will likely have a rectangle about 12x30 inches.
Whisk together the egg with about 1 teaspoon of water and lightly brush onto the pastry.
On one half of the dough, working cross-wise, sprinkle the Parmesan, cheddar, olives and thyme. Gently fold over the other half of the dough and lightly press with the rolling pin. Using a floured pizza cutter or knife, cut the edges so you have an even rectangle. Cut even strips and place on a parchment or Silpat-lined baking sheet, twisting if you wish.
Refrigerate the dough while you preheat the oven to 375° F.
Bake for about 15 minutes, then gently turn the straws over, and bake for 1-2 minutes more. Remove from the oven and let cool slightly. Enjoy warm or at room temperature. Once cooled, the straws may be stored in a tightly sealed container for up to 3 days.
Quantities: The size of the puff pastry rectangle may vary a bit depending on what brand you use, so this recipe generally yields 12 to 15 straws.Make ahead: The cooled straws may be stored in a tightly sealed container for up to 3 days.