Peel and dice persimmons.
Place into a medium-size bowl, and mix in cornstarch.
Stir in honey.
Roll out puff pastry to a 3/16-inch thickness.
Cut into 4-inch squares.
Spread about 1 tablespoon jam on each square of pastry, leaving a 1/2-inch margin at edges.
Then place about 2 tablespoons (or 1 heaping tablespoon) persimmon filling on each square, and fold pastry into a triangle.
Seal edges with tines of a fork.
Cut 2 slashes in top for steam to escape.
Place turnovers on a baking sheet, and put into freezer until pastry is just frozen.
Preheat oven to 400° F.
Brush turnovers with egg, and bake for about 35 minutes, or until golden brown.
Remove from pan, and cool on wire racks.