Preheat the oven to 400F and line two baking sheets with parchment paper.

Roll each sheet of puff pastry out to double the size on a lightly floured surface and brush with melted butter. Sprinkle one with the cheese and the other with the cinnamon sugar.

Fold each of the sheets of puff pastry in half over itself and roll again with a rolling pin to flatten to around the original size of the sheet (before it was folded over). This will press the filling into the dough.

Using a pizza cutter or sharp knife, cut each sheet of puff pastry into around 1/2" strips. Holding each strip at the ends, twist around in opposite directions to form your twist or straw. Place on the prepared baking sheets, brush lightly with butter (you can sprinkle a bit more sugar on the cinnamon ones at this point if desired), and bake for 12-15 minutes, or until golden brown. Cool and serve or store at room temperature for up to a week.