Line a large rimmed baking sheet with parchment paper. Combine blueberries, cornstarch, ½ teaspoon lemon zest, 2 teaspoons lemon juice and a pinch of salt in a medium saucepan. Bring to a boil over medium-high heat; cook, stirring constantly, until the blueberries burst and the mixture is thickened, 5 to 7 minutes. Remove from heat; set aside, uncovered, at room temperature to cool slightly.

Unfold puff pastry and roll out on a lightly floured work surface into a 13-by-10-inch rectangle. Cut the rectangle in half lengthwise; place the halves 1 inch apart on the prepared baking sheet. Place in the freezer, uncovered, to chill until ready to use.

Stir cream cheese, ¼ cup confectioners’ sugar, ½ teaspoon lemon zest and the remaining 1 teaspoon lemon juice and pinch of salt in a small bowl until smooth. Set aside 2 tablespoons of the mixture in a separate small bowl for icing. Remove the puff pastry from the freezer; spread the remaining cream cheese mixture in a 2-inch-wide strip lengthwise down the middle of 1 of the pastry pieces, leaving a ¾-inch border along the edges.

Beat egg and water together in a small bowl. Spoon the blueberry mixture evenly over the cream cheese layer on the pastry; brush the border with egg mixture. Place the remaining pastry piece over the blueberry- and cream cheese-topped piece, pressing the edges firmly to seal. Place in the freezer, uncovered, to chill until firm, about 20 minutes.

Meanwhile, preheat oven to 350°F.

Brush the top of the chilled pastry lightly with the remaining egg mixture (discard any additional remaining egg mixture). Using a very sharp knife, cut 8 small (about ½-inch) slits in the top. Bake until golden brown and evenly puffed, 40 to 45 minutes, rotating baking sheet front to back once. Transfer the baking sheet to a wire rack. Use a spatula to press gently yet firmly on the pastry to flatten slightly. Let cool for 10 minutes.

Whisk milk and the remaining 1 tablespoon confectioners’ sugar into the reserved 2 tablespoons cream cheese mixture until smooth. Drizzle over the warm pastry and sprinkle with the remaining ½ teaspoon lemon zest. Serve warm. Additional reporting by Carrie Myers, M.S. and Linda Frahm