Dust a clean work surface with a sprinkling of flour, and roll half of the puff pastry into a large circle.
Place the largest plate you have (a pizza tray also works) on top of the pastry and tear around the edges to create a clean circle. Repeat with the other half of the pastry.
Preheat the oven to 200°C (400°F) (Gas Mark 6).
Fry the onions and mixed peppers until the onions are translucent.
Add the pre-cooked shredded chicken (to make shredded chicken, simply season and bake some chicken breasts, put it into a bowl and tear it up with 2 forks). Stir in the fajita spice mix and allow to cool while you do the next step.
Transfer one of the sheets to a baking tray, and spread the chicken fajita mix in an even layer, leaving about 1 cm (½ inch) free from the edge. Sprinkle a layer of cheese.
Cover with the second layer of puff pastry. Place an egg cup (or a shot glass) in the center of the pastry and make 8-10 even cuts all the way around the pastry.
Brush the beaten egg over the puff pastry.
Twist each segment twice to make it resemble a sun-like shape.
Bake for 18-22 minutes in the center of the oven, until deep golden brown and no grey patches remain on the pastry.