In a medium saucepan, combine sliced fresh strawberries, unsalted butter, sugar, and cornstarch. Cook over medium heat for 5-10 minutes, stirring occasionally until the mixture thickens and turns syrupy.

In a mixing bowl, beat together cream cheese, sugar, and vanilla extract until light and fluffy, about 3-5 minutes.

In a small bowl, whisk powdered sugar, milk, lemon juice, and vanilla extract until the mixture is smooth and has no lumps.

Thaw your puff pastry sheets and cut them into squares, about 4 inches on each side. Place a spoonful of the strawberry filling in the center of each square, followed by a dollop of the creamy cheese mixture. Fold the pastry over into a triangle shape, ensuring to seal the edges tightly with a fork.

Preheat your oven to 400°F (200°C). Place your assembled turnovers on a baking sheet lined with parchment paper. Brush the tops with an egg wash and bake for 20 minutes or until they puff up and turn golden brown.

Remove the turnovers from the oven and let them cool slightly. Dust them with powdered sugar before serving.