Heat the oven to 400°F (200°C) and line a baking sheet with parchment paper. Beat the softened cream cheese, granulated sugar, lemon zest, lemon juice, and vanilla extract until smooth.

Unfold the cold puff pastry on a lightly floured surface and cut it into eight equal rectangles or squares. Score a smaller rectangle inside each piece, leaving about a 1/2-inch border, then prick the center lightly with a fork without cutting all the way through.

Transfer the pastry pieces to the prepared baking sheet. Spread about 1 tablespoon of cream-cheese filling in the center of each pastry, keeping the border clear, and top with approximately 1 tablespoon of lemon curd.

Beat the egg with the water to make an egg wash. Brush the exposed pastry borders carefully, avoiding the filling and the cut edges as much as possible.

If the pastry has softened, chill the assembled Danish pastries for 10 to 15 minutes. Bake for 15 to 18 minutes, rotating the pan once if needed, until deeply golden, puffed, and set in the center.

Cool the pastries for about 10 minutes before glazing. Whisk the confectioners’ sugar with enough lemon juice to make a pourable glaze, stir in optional lemon zest, and drizzle over the cooled Danish pastries.