Peel, remove pits, and cut peaches into 1/2-inch pieces.

In a saucepan over medium heat, combine peaches, sugars, butter and cinnamon until butter is melted. Cover and cook for 6-8 minutes until peaches reach desired softness.

In a small bowl, mix together 2 Tablespoons water and cornstarch, then add to saucepan. Stir and cover for an additional 1-2 minutes, until peach mixture starts to thicken. Remove from heat and set aside.

Preheat oven to 375 degrees.

Roll out both puff pastry sheets, and cut each sheet into six 3×6 inch rectangles. Evenly split the apple mixture down the middle of six of the rectangles. In the other six sheets, make 3-5 cuts in the puff pastry. Take each puff pastry sheet with peaches and top with a puff pastry sheet that has been cut. Press the seams together using the tines of a fork. Place the hand pies on a baking sheet.

In small bowl, mix together egg white and water. Brush over the top of each hand pie.

In a separate small bowl, mix together sugar and cinnamon, then sprinkle over the top of each pie.

Cook for 15-18 minutes, until pastry starts to brown. Serve warm.