Preheat oven to 400°F (200°C). Line a baking tray with parchment paper.
In a bowl, mix the cooked chicken, cheddar, cream cheese, parsley, and pepper until well combined.
Roll out puff pastry into a rectangle. Place filling down the center third lengthwise.
Using a sharp knife, cut diagonal slits on both sides of the filling, then fold the strips over the filling in a crisscross pattern to create the jalousie.
Brush the top with beaten egg. Transfer to the baking tray.
Bake for 25–30 minutes, or until pastry is golden and crisp. Let cool slightly before slicing.
Notes
For a flavor twist, add sautéed mushrooms or a pinch of paprika to the filling. Can be served hot or at room temperature.