Preheat the oven to 200 C / Gas 6. Line a baking tray with parchment.
Toss apples with brown sugar, almonds, currants, cinnamon and vanilla in a large bowl. Set aside.
Place puff pastry on the baking tray. Roll out lightly to cover the entire tray. Arrange apple filling down the middle of the pastry, lengthways. Fold pastry lengthways around apple mixture. Seal edges of pasty by using a bit of water on your fingers, rubbing the pastry and pinching edges together. Whisk egg and milk together; brush on top of pastry. Cut several vents with a knife or scissors and sprinkle with a few flaked almonds.
Bake in the preheated oven until golden brown, 35 to 40 minutes.