Place the strips in a container, mix with the gyros spice, cover, and refrigerate overnight.
The next day, heat a large pan to medium-high heat.
Add the marinated meat and cook, stirring frequently, for 5 minutes until cooked through. Remove from pan and let cool to room temperature.
Mix the cooled meat with approximately 150g of the grated cheese.
Thaw the puff pastry slices according to package directions.
Roll out each pastry slice slightly.
Divide the meat and cheese mixture evenly among the pastry slices.
Fold each pastry slice over the filling and press the edges together firmly with a fork to seal.
Beat an egg and brush over each pastry pocket.
Sprinkle the remaining cheese over the pastries.
Line a baking tray with baking paper and arrange the pastry pockets on top.
Bake in a preheated oven at 200°C (392°F) using top and bottom heat, or 175°C (347°F) using convection, for 20 minutes until the pastry is golden brown.