Directions:

Thaw pastry at room temperature just until it can be unfolded, about 20 minutes. Preheat oven to 400 degrees F, and line a baking sheet with parchment paper.

Unfold pastry on a lightly floured surface and brush top side with oil. Sprinkle evenly with salt, black pepper, cayenne, cheddar, and 4 tablespoons Parmigiano-Reggiano.

Top with plastic wrap; lay a baking sheet on top, and press cheese and seasonings firmly into dough. Remove sheet and plastic. Cut dough into thirds along seam lines, using a pizza cutter. Cut each third lengthwise into thirds for a total of 9 strips. Cut strips in half crosswise, for a total of 18 sticks.

Put a stick, seasoned side down, on work surface. Grasp an end in each hand and twist several times to make a twist with seasoned side out. Transfer to prepared baking sheet, pressing ends into parchment to keep twists from unrolling. Repeat with remaining sticks.

Sprinkle remaining tablespoon Parmigianao-Reggiano cheese over sticks. Roll sticks gently to pick up and press in any dropped cheese. Twist and stretch as needed to make them similar in length.

Bake 10 minutes; flip once, and continue baking until browned and crisp, 15 to 20 minutes more (if stick droops when you pick it up by one end, it's not done). Serve warm.

The tighter you twist the sticks, the more dense and crisp they will be; a loose twist will result in a softer, more bread-like stick.