Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
In a medium bowl, combine your softened cream cheese, sugar, lemon juice, and vanilla extract. Use a whisk or a spatula to mix it together until it's super smooth and creamy.
Unfold your thawed puff pastry sheet onto your prepared baking sheet or a lightly floured surface. Cut the sheet into 4 equal squares (or 6 smaller rectangles if your pastry is rectangular).
Spoon about a generous tablespoon of the cream cheese filling into the center of each square.
Shape the danishes by taking each corner of the square and gently pulling it towards the center, pressing them together lightly to seal. (Alternatively, do a simple fold-over into a triangle or rectangle).
Crack the egg into a small bowl. Add a tablespoon of water and whisk it up for the egg wash.
Brush the tops and exposed pastry edges of each danish with the egg wash.
Bake for 12-15 minutes, or until the danishes are puffed up, golden brown, and the filling looks set.
Let them cool on the baking sheet for a few minutes before transferring them to a wire rack.