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1
Preheat oven to 400 degrees F (200 degrees C).
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2
Line a baking sheet with parchment paper or a silicone baking mat.
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3
Place a sheet of frozen puff pastry dough onto a floured work surface and allow dough to thaw just until it can be unfolded.
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4
Unfold dough into a flat sheet; brush top of puff pastry dough with olive oil.
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5
Season with salt, black pepper, and cayenne pepper.
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6
Sprinkle white Cheddar cheese and 1/4 cup Parmigiano-Reggiano cheese onto the dough, covering the surface.
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7
Top with a piece of plastic wrap; press cheese and seasonings firmly into the dough with your fingers or by laying a sheet pan onto the dough over the plastic and pressing it down.
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8
Remove plastic and use a pizza cutter or sharp knife to cut the dough down the seam lines into thirds; cut each third lengthwise into thirds for a total of 9 breadsticks.
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9
Pick up a dough strip, place it seasoned side down on the work surface, and twist from both ends 8 or 9 times to make a rolled tube of dough with the seasoned side out.
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10
Place breadsticks onto prepared baking sheet.
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11
Sprinkle remaining 1 tablespoon Parmigiano-Reggiano cheese over the sticks.
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12
Roll the sticks lightly to even up their shapes and pick up and press any dropped cheese onto the surfaces.
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13
Bake in the preheated oven for about 10 minutes; flip and continue baking until breadsticks are browned and crisp, 10 to 20 more minutes.
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14
If you pick up a stick by one end and it droops, bake for several more minutes.
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15
Cool on a wire rack before serving.
