Simple, yet elegant, these crisp yet airy straws can be made days ahead of time, making this an ideal party snack.
Preheat oven to 425 degrees. Line 2 baking sheets with parchment.
On a lightly floured surface with a lightly floured rolling pin, roll puff pastry into a 12-by-16-inch rectangle. With the long side facing you, lightly brush bottom half of rectangle with some of the beaten egg. Sprinkle 1/4 cup Parmesan and the salt on top half. Fold bottom half over top half. Gently roll dough to seal.
Cut rectangle lengthwise into thirds. (You should have three 2-by-16-inch strips.) Sprinkle remaining 1 tablespoon Parmesan on 1 strip, poppy seeds on another, and cayenne on remaining strip. Cut each strip lengthwise into eight 1/4-by-16-inch strips.
Transfer strips to baking sheets, spacing 1 inch apart. Working with 1 strip at a time, hold each end with your fingers, and carefully twist strip in opposite directions, forming a spiral. Press ends of strips against parchment to prevent unraveling. Freeze or refrigerate until strips are very firm and cold, about 15 minutes.
Bake 1 sheet at a time, rotating halfway through, until straws are golden brown and cooked through, 12 to 14 minutes. Transfer straws to wire racks, and let cool.
Straws can be stored at room temperature for up to 2 days.