Thaw the puff pastry according to the package directions, keeping it cold rather than letting it become soft or warm. Heat the oven to 400°F (200°C) and line a baking sheet with parchment paper.

Beat the softened cream cheese, granulated sugar, egg yolk, vanilla extract, and fresh lemon juice until completely smooth. Cut the cold pastry sheet into 8 equal squares, then lightly score a smaller square inside each piece, leaving about a 1/2-inch edge without cutting all the way through.

Arrange the pastry squares on the prepared baking sheet and spoon about 1 tablespoon of filling into the center of each square. Keep the filling away from the scored border, then brush the pastry edges with beaten egg.

Bake for 15–18 minutes, or until the pastry is deeply golden and puffed and the cream cheese filling is set. Cool the pastries for several minutes before serving.

For the optional glaze, whisk the confectioners’ sugar with the milk or heavy cream until smooth, adding a little more liquid as needed. Drizzle the glaze over the cooled Danish.