Making your own cheese twists (or straws or sticks) is easier than you might imagine. Here we rely on store-bought puff pastry brushed with a quick rosemary-pepper oil and sharp Cheddar cheese. Keep the pastry well chilled, or it will be sticky. You can make these cheese twists several hours ahead of time. Or make them a day ahead of time and store in a tightly sealed container; then reheat for a few minutes in a 275° oven.
First, make the flavored oil: In a small saucepan, heat the olive oil, rosemary, and pepper over low heat until just simmering. Remove from the heat and let cool to room temperature. You can make this oil several days ahead of time.
Next, make the twists: Preheat your oven to 400°. Remove the pastry from the freezer and thaw until it's pliable but still chilled. Lay the sheets on a well-floured surface and brush with flavored oil. Now take 1 tablespoon of the rosemary and ½ cup of the Cheddar and sprinkle them evenly over both sheets of pastry. Gently press the toppings into the pastry. Flip the pastry over and repeat with the remaining oil, rosemary, and cheese.
Using a pizza cutter or a small, sharp knife, cut the pastry lengthwise into strips about ½ inch wide. Flour your hands lightly, and, holding a strip at each end, twist to create a spiral. Place the twisted strips on ungreased cookie sheets, pressing the ends lightly to keep them from untwisting. Sprinkle very lightly with the cayenne, if you like. If the pastry has gotten warm and looks limp, return it to the refrigerator for about 15 minutes.
Bake on the middle and top racks for 8 minutes. Gently flip the twists over and bake until golden brown, 5 to 7 minutes more. Remove from the oven and let cool. Serve warm or at room temperature.