Lightly flour a clean, flat surface and roll the sheet of puff pastry to an 1/8th of an inch in thickness. Try to keep it approximately the shape of a rectangle for smoother edges.
Sprinkle the cheese, lemon zest, ground pepper, and salt evenly over the long top half. Fold the bottom half over, gently pressing the two sides together to seal. Use a very sharp knife to cut 1/2-3/4 inch wide strips.
Handling one strip at a time, take one end in each hand and carefully twist them in opposite directions to form a tight spiral. Place them on a parchment paper-lined baking sheet, pressing the ends down firmly to discourage them from uncurling. Repeat with the remaining dough, placing the twists about 1 inch apart. Move the entire batch into the freezer and let rest for 30 minutes before baking.
Once the straws are nearly done chilling, begin preheating your oven to 425 degrees F.
Move the frozen baking sheet immediately into the oven and bake until the straws are golden brown all over(13-16 minutes). Transfer to wire racks and let cool completely before eating.