Preheat oven to 400 degrees F (200 degrees C).
Prepare the Puff Pastry (2) by cutting each sheet into three rectangles, then cutting those in half to make 6 squares. Cut each square at a diagonal to create 12 angles triangles. Set aside until needed.
Dice the Granny Smith Apple (2) and put the cut apples into a bowl with the juice of Lemon (1/2). This will keep them from browning!
Prepare the apples by melting the Butter (2 tablespoon) in a skillet. Add the apples and cook for 5 minutes over medium heat, stirring occasionally. Add the Brown Sugar (5 tablespoon) and Pumpkin Pie Spice (2 teaspoon) and allow to cook until the sugar is melted and coats the apples.
Add the Corn Starch (1 tablespoon) and stir in. Add the Apple Cider (1/4 cup) and cook until thickened, about 2 minutes.
Prepare the turnovers by spooning filling into half of the triangles, then topping with the matching remaining half. Seal the edges with a fork, brush with the Egg (1) then bake for 15 minutes or until puffy and golden.
Top with your choice of powdered sugar, caramel, icing, or remaining apples.