Place the cherries, juice and sugar into a heavy-bottomed pot and heat over medium. Simmer for about 10 minutes, or until the cherries soften slightly.
Mix the cornstarch and 2 tsp. of water together in a small bowl. Once the compote has cooked, add the cornstarch a bit at a time while stirring. Simmer for 1 minute.
Preheat your oven to 425° F.
Using a sharp knife, cut the puff pastry into 4 squares.
In a small bowl, beat the egg and 1 Tbsp. water until smooth. Using a pastry brush apply the egg wash around the perimeter of the square.
Place about a tablespoon of the compote into the center.
Fold the dough over to create a triangle and match up the tips. Press gently to seal. Use a fork to press the seams together. Place the turnovers onto a lined tray and chill in the refrigerator for 10 minutes.
Once the turnovers are cold, mix the milk or cream with the remaining egg wash. Brush the top and sides of the turnovers with the egg wash. With a sharp knife, make 1 or 2 small openings on the top of each turnover. Sprinkle with a bit of sugar.
Bake for 15 minutes, or until golden brown. Once done, transfer to a cooling rack. Let cool before serving.
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