1. Preheat oven to 375 degrees, with racks in upper and lower thirds. Lightly flour a work surface and rolling pin; roll out puff pastry to a 10-by-18-inch rectangle. Brush with 1 tablespoon butter, sprinkle with 3 tablespoons Parmesan, and season with pepper. Gently roll over dough to adhere. Flip dough and repeat with more butter, cheese, and pepper.

2. Cut dough in half lengthwise, then cut each piece into 1/2-inch-wide strips. Arrange in a single layer on two parchment-lined baking sheets and bake until pastry is golden and puffed, about 7 minutes, rotating sheets halfway through. Let cool completely.