In a large saucepan, mash together the cherries and sugar (without turning the burner on). Let it stand for 15-20 minutes. Then stir in the cornstarch until blended. Bring the mixture to a boil over medium heat. Cook and stir for for 2 minutes or until thickened. Remove it from the heat and stir in the cinnamon. Let cool.
Preheat oven to 375 degrees. Unwrap the pastry dough and cut into 8 total squares.
Place a heaping tablespoon of the cherry mixture in the center of each square. brush the edges of the squares with the egg white and fold over (making it a triangle) to enclose the pie filling. Dust the top with the sparkling sugar. (you may also use a glaze or icing on top instead of the sparkling sugar)
Bake on an un-greased baking sheet for 20-25 minutes, or until puff pastry is golden brown. Let cool on a wire rack.