01 - Preheat oven to 400°F. Line a baking sheet with parchment paper.
02 - In a small pan, melt butter over medium heat. Add diced apple, brown sugar, cinnamon, and lemon juice. Cook, stirring frequently, for 3–4 minutes until apples are tender and coated in a syrupy glaze. Remove from heat and let cool.
03 - In a mixing bowl, combine cream cheese, granulated sugar, and vanilla extract. Stir until smooth and creamy.
04 - Roll out the puff pastry sheet on a lightly floured surface and cut into 8 equal squares.
05 - Arrange squares on the prepared baking sheet. Using a sharp knife, score a border approximately ⅜ inch from the edge of each square, being careful not to cut all the way through the dough.
06 - Spread 1 tablespoon of cheese filling in the center of each square. Top with a spoonful of the cooled apple mixture.
07 - Brush the exposed pastry edges generously with beaten egg to promote golden browning.
08 - Bake for 18–20 minutes until pastries are puffed and deep golden brown.
09 - Cool danishes on the baking sheet for 10 minutes. Whisk powdered sugar with milk until a drizzle-consistency icing forms. Drizzle over warm danishes if desired.