Combine the pitted cherries, granulated sugar, cornstarch, water, and lemon juice in a medium saucepan. Stir well to coat the fruit.
Cook over medium-high heat until the mixture reaches a boil. Reduce the heat to low and simmer for 8 minutes, stirring often, until the liquid is thick and glossy.
Remove the pan from the heat and stir in the almond extract. Transfer the filling to a bowl and let it cool completely.
Place one thawed puff pastry sheet on a lightly floured surface. Roll it into a 10-inch (25-cm) square, then cut it into four 5-inch (12-cm) squares. Repeat with the second sheet.
Spoon 2 to 3 tablespoons of the cooled cherry filling into the center of each square.
Brush the edges of each square with the beaten egg. Fold the dough over the filling to create a triangle. Press the seams together with your fingers, then crimp the edges with a fork.
Place the turnovers on a parchment-lined baking sheet. Cut two small slits into the top of each pastry. Place the baking sheet in the freezer for 15 to 20 minutes to chill the dough.
Preheat the oven to 400°F (200°C) while the pastries chill.
Remove the baking sheet from the freezer. Brush the top of each turnover with the remaining egg wash and sprinkle with turbinado sugar. Bake for 22 to 24 minutes until deep golden brown. Cool on a wire rack before serving.