In a skillet, saute apples with butter, sugars, cinnamon and apple pie spice until soft, about 4 minutes. Mix cornstarch and water together and add to mixture. Cook 1 more minute. Set aside to cool (make sure you give this plenty of time to cool. I give it at least 1 hour).
Using thawed puff pastry dough, roll out onto a floured work surface and roll dough into about a 12X18 inch rectangle. Cut into 6 equal rectangles. Scoop apple filling onto the middle of the rectangle. Fold dough over and press down on all 4 sides to seal. Repeat with all rectangles.
Place on a cookie sheet lined with parchment paper. Brush tops with the melted butter and sprinkle with sugar.
Bake at 375 degrees for about 20 minutes. Top with ice cream and eat while hot. (You need to pretty much serve these when they come out of the oven if you want them warm. They cool down pretty fast.) Makes 6 servings.