Preheat oven to 400 and line a baking sheet with parchment paper.
Place the pastry onto a floured surface (or an additional sheet of parchment paper), and using a rolling pin, roll the dough, so it's about 15" in length.
Spread oil on the surface of the dough.
Season with salt, pepper, and cayenne powder.
Sprinkle shredded white cheddar cheese and 1/4 cup of grated Parmesan cheese on the puff pastry dough.
Top the dough with a piece of plastic wrap and use a rolling pin to press the cheese into the dough. Remove the plastic wrap and discard.
Use a pastry or pizza cutter to cut the dough. First, cut the seams so you have three rectangles. Then cut each rectangle into thirds.
Twist each piece of dough about 8-9 times and place onto a prepared baking sheet lined with parchment paper.
Sprinkle the remaining grated Parmesan on twisted breadsticks.
Bake the bread for 10 minutes. Flip the breadsticks over and bake for an additional 10 minutes.
If desired (and depending on the level of crispiness you would like) return the pan to the oven for 5-10 minutes for crispy breadsticks. Ideally, you don't want a droopy breadstick, but it's a personal preference. See notes for cooking instructions.
Cool slightly and serve crispy breadsticks warm.
Notes
Important Tips
If you want them crispier, cut them thinner, so maybe get 18 (double) out of the batch vs. the 9 I made.If the sticks are wider, it’s more bread-like, and thinner strips will be denser and crispier.Looser, and you get more of a bread-like twist; tighter, and it’s crispier. I also think cooking it longer makes a difference!Recipe as shown: I baked mine for 25 minutes in total. 10 minutes. Flip. 10 minutes more. Flip. 5 minutes. Done.