Cook the blueberries. Place the blueberries, sugar, and salt in a small saucepan over low heat. Cook gently, stirring occasionally, until the berries release their juices and the sugar dissolves.
Thicken the filling. Once the mixture begins to simmer, gradually stir in the fine semolina. Continue cooking, stirring frequently, until the filling thickens and the grains soften. The total filling cook time is approximately 10 minutes, depending on the berries. Remove from the heat and stir in the vanilla extract.
Cool the filling. Set aside until completely cool, about 30 minutes or longer as needed. Transfer to a shallow bowl to help it cool more quickly.
Prepare the oven and pastry. Preheat the oven to 350°F (180°C). Line a baking sheet with parchment paper. On a lightly floured surface, roll the cold puff pastry into an even square, then cut into four equal squares.
Fill the squares. Whisk the egg and milk together in a small bowl. Lightly brush two adjacent edges of each pastry square with the egg wash. Divide the cooled blueberry filling evenly among the squares, leaving a clear border for sealing.
Fold and seal. Fold each square diagonally over the filling to form a triangle. Press the edges together, then gently crimp with a fork. Place on the prepared baking sheet, leaving space between the turnovers.
Brush and vent. Lightly brush the tops with egg wash. Cut two or three small slits through the top layer of each turnover to allow steam to escape.
Bake. Bake for about 20 minutes, or until puffed, golden brown, and cooked through underneath. Add extra baking time if needed.
Cool and serve. Let cool for about 10 minutes, transferring to a wire rack after the first few minutes. Dust with powdered sugar, if desired, and serve warm.
