Defrost the puff pastry overnight in the refrigerator (or according to the package directions). Unroll the defrosted puff pastry and place on the counter top for about 20 minutes.
Meanwhile, core the apples. Cut each apple in half and slice as thinly as you can. Throw the apple slices into a bowl.
Add lemon juice, sugar, nutmeg, cinnamon and a pinch of salt. Gently stir together and let them sit for a few minutes (about 5 minutes), they will become juicy.
Preheat oven to 400 degrees F. Cut the puff pastry sheets in half. Spray a baking sheet with non-stick cooking spray, then gently place the puff pastry rectangles on the baking sheet. Gently brush with melted butter.
Lay the apple slices in a straight line on top of the puff pastry, overlapping them as you go.
Place the baking sheet on the middle rack of the oven and bake for about 20 minutes (keep an eye on them).
Remove the tarts from the sheet as soon as you pull them from the oven and place on a serving platter. Dust with powdered sugar just before serving. Cut into thin slices. You can serve with vanilla ice cream or whipped cream.