In a medium saucepan, melt the unsalted butter over medium heat. Once melted, add the diced Granny Smith apples and cook for about 3 minutes, stirring occasionally.

Stir in granulated sugar, ground cinnamon, ground allspice, ground nutmeg, and kosher salt. Continue cooking until the apples are softened and caramelized, about 5–7 minutes.

Remove the apple mixture from heat and set it aside to cool to room temperature.

Roll out the puff pastry into an 11-inch square on a lightly floured surface. Cut the pastry into 4 equal squares.

Place a generous spoonful of cooled apple filling on one half of each pastry square, leaving a ½-inch border to seal the edges later. Brush the borders with egg wash.

Fold the pastry over the filling to create a pocket. Seal the edges with a fork and transfer the turnovers to a parchment-lined baking sheet.

Preheat your oven to 400°F (200°C) and refrigerate the assembled turnovers for 20 minutes.

Brush the tops of the turnovers with egg wash and cut a few small vents in the tops.

Bake in the preheated oven for 20–22 minutes, or until golden brown and puffed up.

While the turnovers cool slightly, mix powdered sugar, milk, and vanilla extract until smooth for the glaze. Drizzle over warm turnovers.