Combine blackberries, sugar, water, and lemon juice in a medium saucepan. Cook for 3-4 minutes over medium-low heat until syrupy.

Stir in cornstarch, cook 1-2 more minutes until thickened. Cool for 10 minutes.

Preheat oven to 400°F (200°C) and line a baking sheet with parchment paper.

Roll out thawed puff pastry on a floured surface and cut into 4 squares.

Spoon 2 tablespoons of filling onto each pastry square. Be careful not to overfill.

Brush edges with egg wash, fold over to create triangles, and crimp edges with a fork.

Create steam vents on top of each turnover with a knife or fork.

Bake for 18-21 minutes until golden-brown and flaky.

Whisk together powdered sugar and cream for the glaze until smooth.

Drizzle the glaze over the cooled turnovers and let set before serving.