Cheese Straws

Line 2 baking sheets with parchment paper. In a medium bowl, gently stir together the cheddar, parmesan, and cayenne, and set aside. In a small bowl, beat together the eggs and 1 teaspoon water until thoroughly combined.
2
Unfold the puff pastry onto a lightly floured work surface. If the pastry comes in a single large sheet, cut it in half crosswise. Roll out each piece of puff pastry to a roughly 8-by-10-inch sheet. Brush one of the pieces with egg wash, then evenly sprinkle over half the cheese mixture. Sprinkle with half the black and white sesame seeds. Gently press the toppings into the puff pastry with a rolling pin, then roll out the sheet to roughly 10 by 12 inches.
3
Using a sharp, lightly floured knife or pastry wheel, cut the puff pastry sheet crosswise into 12 (10-by-1-inch) strips. Twist the ends of each strip into a spiral and transfer to one of the prepared baking sheets. Lightly brush any exposed puff pastry with more egg wash and sprinkle with flaky salt, if using. Transfer the baking sheet to the refrigerator and chill until the cheese straws are firm, at least 30 minutes and up to 12 hours (if chilling for more than 2 hours, cover the cheese straws with plastic). Repeat with the remaining puff pastry, cheese, and sesame seeds.
4
Meanwhile, preheat the oven to 400°F. Once they are well chilled, bake the cheese straws in batches, 8 to a baking sheet, spaced about 1 inch apart. Bake, rotating halfway through, until the cheese straws are puffed, lightly golden, and lacy at the edges, 13 to 15 minutes.
5
Allow to cool completely on the baking sheets before serving.