Preheat oven to 400 degrees F. For filling, in a medium bowl toss peaches with sugar; set aside for 5 minutes or until syrupy. Strain peach syrup (add enough water to equal 1/3 cup). Add to a small saucepan and whisk in lemon juice, cornstarch, and cinnamon. Cook and stir over medium heat until very thick. Remove from heat; cool slightly. Add to peaches; toss to combine.
On a lightly floured surface, roll one pastry sheet at a time to a 12x10-inch rectangle (cover remaining pastry sheet to prevent it from drying out). Cut rolled pastry in half to make two 10x6-inch rectangles. Fill each rectangle with about 1/2 cup filling. For egg wash, lightly beat egg with a little water. Brush pastry edges with egg wash. Fold short side of dough over filling. Crimp edges with a fork to seal. With a large spatula, transfer to a parchment-lined
Lightly brush tops of turnovers with egg wash. Bake 15 to 17 minutes or until golden and puffed. While first turnovers bake, roll and fill remaining turnovers. Bake as above. Cool slightly. To serve, cut each turnover in half. Serve with ice cream, if desired. Makes 8 servings.