Preheat the oven to 400°F. Prepare a baking sheet lined with parchment paper for easy cleanup.

In a medium bowl, mix cream cheese, shredded rotisserie chicken, mozzarella, sharp cheddar, and buffalo sauce until well-blended.

Roll out the thawed puff pastry on a floured surface to a rectangle measuring 9×12 inches.

Spread the chicken mixture evenly over the pastry, leaving a ½-inch border, and brush the border with beaten egg.

Roll the pastry tightly into a log, slice into 12 equal pieces, and place on the prepared baking sheet.

Brush the tops with remaining beaten egg and bake for 15-18 minutes until golden brown.

Remove from the oven, top each roll-up with a bit of reserved chicken mixture, and bake again for an additional 6-8 minutes.

For air fryer method, assemble as directed and air fry at 325°F for 10-12 minutes, adding reserved mixture halfway through.