Position a rack in lower third of oven and preheat to 400°F. Line a baking sheet with a piece of parchment paper. Combine apples, jam and cornstarch in a medium bowl. Mix sugar and cinnamon in a separate small bowl.
On a lightly floured surface, roll out puff pastry into an 8-by-12-inch rectangle. Cut pastry into 6 4-inch squares with a sharp knife or pizza cutter.
Spoon some apple mixture into center of each square, leaving a 1-inch border. Brush borders with beaten egg. Fold each square into a triangle and press edges with tines of a fork to seal (be sure to seal tightly). Using a sharp paring knife, cut 2 small steam vents in top of each turnover. Sprinkle each turnover with cinnamon sugar. Place turnovers on lined baking sheet.
Bake until golden and puffed, about 20 minutes. Serve warm.
This recipe also appeared in the October 2008 issue.