Preheat oven to 375℉. Line a large baking sheet with parchment paper. Set aside.
In a medium skillet, melt butter over medium heat. Stir in the diced apples, brown sugar, cinnamon, salt, and nutmeg. Cook the apples, stirring occasionally, for about 5-7 minutes, or until mixture is bubbly and apple start to soften.
Add the cornstarch and cook for another 1-2 minutes, or until mixture thickens. Remove from heat and let cool slightly.
On a lightly floured surface, roll out the puff pastry sheets and cut into four squares.
Spoon 2-3 tablespoons of the apple mixture onto one side of each square, leaving about a 1" border around the edges. Brush the edges lightly with milk, then fold each square over to form a triangle. Press the edges with a fork to seal
Place each triangle onto the prepared baking sheet and refrigerate for 20-30 minutes. (see note below) If not refridgerating, move on to the next step.
Remove the pan from the refrigerate and brush tops with the remaining milk.
Bake for 18-20 minutes, or until the turnovers are golden brown and flaky. Let cool completely before adding the glaze.