Unfold puff pastry sheets onto a clean, lightly floured work surface. If the puff pastry box comes with only 1 sheet, then cut it in half. Use a rolling pin to lightly roll the dough out, just enough to smooth any creases from the dough.
In a small bowl whisk together the egg and 1 tablespoon water. Use a pastry brush to spread the egg wash over one sheet of puff pastry. Sprinkle half the cheese over the egg wash. Top with ½ the chives and cayenne. Season with salt and pepper.
Layer the second sheet of puff pastry over the top of the cheese and press gently to adhere the edges.
Brush the top with egg wash and sprinkle the remaining cheese, chives, and cayenne over the top.
Lightly sprinkle the rolling pin with flour and then gently roll the rectangle of cheesy puff pastry out so it’s ¼” thick.
Cut the puff pastry into ½” thick strips. For shorter cheese twists, cut the strips in half crosswise (optional).
Working one strip at a time, carefully twist each strip several times. Line baking sheets with parchment paper or silicone baking mats. Place strips 1” apart on the baking sheet. Repeat with the remaining strips, working in batches if needed.
Cook until the twists are golden brown, rotating the pans halfway through, about 15 to 20 minutes. Let cool completely and serve.