In a saucepan, combine the diced apples with sugar, cinnamon, and star anise. Simmer until the apples begin to soften.
Add the butter and a cornstarch slurry, stirring until the mixture thickens.
Remove from heat and allow the filling to cool to room temperature.
Roll out the puff pastry sheet and place it on a lined baking tray.
Spoon the apple filling down the center of the pastry.
Fold and Seal
Fold the pastry over the filling, sealing the edges.
Cut small slits on top and brush with melted butter.
Bake until the pastry is golden, puffed, and cooked through.