1 cup finely grated Parmigiano-Reggiano (about 4 ounces)
½ teaspoon cayenne pepper
2 sheets frozen puff pastry, preferably all-butter, thawed
All-purpose flour, for dusting
2 large eggs, lightly beaten
Preheat oven to 425 degrees. Combine cheese and cayenne in a bowl.
Lay each puff-pastry sheet flat on a lightly floured work surface. Roll out two 11-by-16-inch rectangles. Dividing evenly, brush with some of beaten eggs and sprinkle with cheese mixture. Using a pastry cutter or sharp paring knife, trim long ends to make even, then cut each rectangle crosswise into fifteen 1/2-inch-wide strips.
Working with one at a time, twist each strip into a spiral and transfer to parchment-lined baking sheets, 1 inch apart. Using your thumb, press ends of strips onto parchment to prevent unraveling during baking. Chill until firm, at least 30 minutes.
Bake until pastry is golden, rotating sheets halfway through, 10 to 15 minutes. Let cool completely on sheets on wire racks before serving or storing.
Sesame-Poppy
Combine 2 tablespoons each sesame seeds and poppy seeds with 1/4 teaspoon coarse salt in a bowl. Sprinkle on pastry strips instead of cheese-cayenne mixture.
Tomato-Rosemary
Omit egg wash and cheese-cayenne mixture. Combine 3 tablespoons tomato paste and 1 tablespoon extra-virgin olive oil in a bowl. Brush evenly on pastry strips, then sprinkle with 1 tablespoon chopped fresh rosemary.
Pecorino-Black Pepper
Replace Parmigiano-Reggiano with an equal amount of Pecorino Romano, and cayenne pepper with freshly ground black pepper. Sprinkle mixture on pastry strips.