Line 3 large baking sheets with parchment paper. Thaw the pastry sheet at room temperature covered by a clean kitchen cloth, about 30 minutes. While the pastry is thawing, combine cheese, olive oil, garlic, oregano, salt and cayenne in a small mixing bowl. Stir well to combine. In a clean small mixing bowl, beat the egg with a fork. On a lightly floured surface, gently unfold the pastry.
Sprinkle the pastry lightly with flour and using a rolling pin, roll into a 14 by 10-inch rectangle. Brush the top of the pastry with a beaten egg. Cut in 1/2 lengthwise to form 2 (7 by 10-inch) rectangles. Spread the herb-cheese mixture with the back of a spoon evenly across 1 rectangle. Lay the second rectangle across the coated piece, egg side-down. With the rolling pin lightly roll the 2 sheets together to seal. With a large knife cut crosswise into strips, about 1/3-inch wide each. (Alternately, you can use a pizza wheel to cut the strips.) One at a time, grab the ends of each strip and twist in opposite directions to form a spiral. Transfer to the prepared baking sheets. Bake until light golden brown, about 10 minutes. Remove from the oven and let cool on baking sheets until cool enough to handle. Serve either warm or at room temperature.