Heat the oven to 400°F (200°C) and line a baking sheet with parchment paper. Set the softened cream cheese aside while the oven preheats, but keep the puff pastry cold until you are ready to shape it.

Beat the cream cheese, granulated sugar, egg yolk, and vanilla extract until smooth and creamy. Scrape the bowl once or twice so the mixture is evenly combined and free of large cream cheese lumps.

Unfold the cold puff pastry and cut it into 8 equal rectangles or squares. If the pastry begins to soften or feel sticky, place it in the refrigerator for a few minutes before continuing.

Score a smaller border inside each pastry piece, leaving about 1/2 inch around the edge, and be careful not to cut all the way through. This inner line helps define the center while allowing the outside rim to puff beautifully.

Spoon approximately 1 tablespoon of cream cheese mixture into the center of each pastry. Add several blueberries to each piece, keeping the fruit away from the outside edge so the juices do not escape too easily.

Whisk the remaining large egg with 1 tablespoon of water, then brush the exposed pastry border with the egg wash. Transfer the pastries to the parchment-lined baking sheet, leaving space between them.

Chill the assembled pastries for 10–15 minutes if the puff pastry has become soft. Bake for 18–22 minutes, or until the pastry is deeply puffed and golden brown and the cream cheese filling is set.

Cool the pastries on the baking sheet for at least 10 minutes. Stir the confectioners’ sugar with enough milk or lemon juice to make a pourable glaze, then drizzle it over the warm or cooled pastries before serving.