Preheat oven to 400°F (200°C). Line two baking sheets with parchment paper or silicone liners.
Using an electric mixer on medium speed, beat the cream cheese, sugar, egg yolk, lemon juice, and vanilla until smooth.
Roll one sheet of puff pastry into an approximately 10-inch (25.5cm) square. Cut into 9 squares.
Transfer the squares to the prepared pan. Use a fork to dock the pastry, leaving a 1 & 1/2 inch (3.8cm) border. You don't need to poke holes all the way through; just lightly poke with a fork.
Brush each pastry with the egg white.
Top each square with about a tablespoon of cream cheese mixture. (A #50 scoop works very well.) Place it just in the center; it will spread as it bakes.
Bake for 12 to 16 minutes, or until the pastries are lightly browned.
Place the pans on wire racks to cool. Serve warm or at room temperature.
To make the glaze:
Stir together the confectioners’ sugar, 1 tablespoon milk/cream, and vanilla. Add more milk or cream, a small amount at a time until the glaze is thick but pourable.
Drizzle the glaze over the pastries before serving.
Notes
These danishes are best enjoyed freshly baked but can be stored in an airtight container in the refrigerator for a couple of days.