Preheat oven to 425 degrees. Line a baking sheet with parchment paper and set aside.
In a saucepan over medium heat, add cherries, granulated sugar, lemon juice, cornstarch, and cinnamon. Stir to combine and bring to a simmer. Reduce heat to medium-low and cook for 8-10 minutes, or until mixture has thickened. If needed, add 1-2 tablespoons of water (if cherries are not releasing enough juice). Remove from heat and allow to cool.
On a lightly floured surface, roll out puff pastry sheets to approximately 12 inch squares. Cut each sheet into four squares.
Spoon a scant ¼ cup of pie filling onto a corner of each square, avoiding ½ an inch around the edges. Fold the opposite corner of each puff pastry over to cover filling. This will form a triangle. Press the edges with a fork to seal.
In a small bowl, whisk egg and 1 tablespoon of water to create an egg wash. Brush tops and edges of each turnover with egg wash.
Sprinkle the tops with turbinado sugar and slice a vent into each turnover.
Transfer turnovers to parchment lined baking sheet. Bake for 19-22 minutes, or until turnovers are golden brown.
*Optionally, use 2 cups of store bought pie filling instead. Cherry pie filling can be substituted with blueberry pie filling or apple pie filling.
Egg wash can be substituted with 2 tablespoons of heavy cream instead, with the same result.
Turbinado sugar can be substituted with granulated sugar.