Prepare the filling by combining blackberries, sugar, water, salt, and lemon juice in a medium saucepan. Simmer over medium-low heat for 3-4 minutes until blackberries soften. Stir in cornstarch and simmer for another 1-2 minutes until thickened. Let cool.
Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper. Roll out the thawed pastry on a floured surface and cut into 4 squares per sheet.
Place about 2 tablespoons of cooled blackberry filling in the center of each square.
Whisk the egg and water together for the egg wash, then brush the edges of each square. Fold each square diagonally to form a triangle, sealing the edges with a fork. Transfer to the baking sheet.
Cut 3 slits in the top of each turnover to allow steam to escape. Bake for 18-21 minutes until golden brown. Let cool before glazing.
For the glaze, whisk powdered sugar and heavy cream until smooth. Drizzle over cooled turnovers and let set before serving.
Notes
Feel free to use frozen blackberries if fresh ones are not available.