Preheat the oven to 400°F (200°C) and line a baking tray with parchment paper.
Cook the butter, diced apples, brown sugar, cinnamon, nutmeg, and vanilla in a saucepan over medium heat until the apples begin to soften.
Mix the cornstarch with the water and stir it into the apples. Continue cooking until the juices become glossy and thick, then allow the filling to cool.
Roll the puff pastry lightly if needed and cut it into eight equal rectangles. Spoon the cooled apple mixture onto one side of each rectangle, leaving space around the edges.
Fold the pastry over the filling, seal with the tines of a fork, and transfer each pastry to the prepared baking tray.
Bake for 22–25 minutes, or until the pastry is deeply puffed and evenly golden.
Cool slightly before finishing with the optional vanilla icing, then serve while still warm.