Prepare the Blackberry Filling: In a small saucepan, combine the blackberries, granulated sugar, water, and salt. Heat over medium until the mixture begins to bubble, about 5 minutes. Stir occasionally to prevent sticking.

Thicken the Filling: In a small bowl, mix the lemon juice and cornstarch until smooth, then add to the blackberry mixture. Continue cooking for an additional 1-2 minutes until the filling reaches a thicker consistency. Remove from the heat and allow it to cool completely.

Prepare the Puff Pastry: Preheat your oven to 400°F (200°C). Place the thawed puff pastry sheets on a surface dusted with flour. Cut each sheet into four equal squares, resulting in eight squares in total.

Fill and Fold the Turnovers: Spoon about 1-2 tablespoons of the cooled blackberry filling onto the center of each puff pastry square. Fold each square into a triangle shape and use a fork to press down along the edges, sealing them tightly.

Egg Wash and Bake: In a small bowl, whisk the egg with 1 tablespoon of water. Lightly coat the tops of the turnovers with a layer of egg wash. Place the turnovers on a parchment-lined baking sheet and bake for 18-20 minutes, or until golden brown and puffy.

Make the Glaze: In a small bowl, mix the powdered sugar and heavy cream (or milk) until smooth. Add more cream or milk as needed for a drizzle consistency.

Drizzle and Serve: Once the turnovers have cooled slightly, drizzle them with the glaze. Serve warm or at room temperature.