Select the “CONVECTION” function and preheat the Russell Hobbs Air Fryer Oven to 180 degrees.

Line a baking sheet that fits into the cooking cavity with parchment paper or a silicone baking mat.

Place a sheet of frozen puff pastry dough onto a floured work surface and allow dough to thaw just until it can be unfolded.

Unfold dough into a flat sheet; brush the top of the puff pastry dough lightly with olive oil. Sprinkle salt, black pepper, and cayenne pepper onto the puff pastry sheet.

Grate and sprinkle the white Cheddar cheese and 3 tbsp Parmigiano-Reggiano cheese onto the dough, covering the surface. 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.

Remove the plastic and use a sharp knife to cut the dough into three equal parts; then divide each third into three for a total of 9 breadsticks. Sprinkle a tablespoon of Parmigiano-Reggiano cheese over the sticks.

Roll the sticks lightly to even up their shapes, pick up and press any dropped cheese onto the surface.

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. Place the rolled breadsticks onto your prepared baking sheet.

Sprinkle the remaining Parmigiano-Reggiano cheese over the sticks. Roll the sticks lightly to even up their shapes finishing with any dropped cheese over the tops.

Bake in the preheated oven for about 5 minutes; flip and continue baking until the breadsticks are browned and crisp, about 5 more minutes. If you pick up a stick by one end and it drops, bake until sturdy. Allow them to cool down on a rack before serving.