01 - Preheat oven to 400°F. Line a baking sheet with parchment paper and set aside.
02 - Melt butter in a small pan over medium heat. Add diced apple, brown sugar, cinnamon, and lemon juice. Cook, stirring frequently, for 3–4 minutes until apples are soft and coated in a syrupy glaze. Remove from heat and let cool completely.
03 - In a mixing bowl, combine softened cream cheese, granulated sugar, and vanilla extract. Beat until smooth and creamy.
04 - Roll out the puff pastry sheet on a lightly floured surface and cut into 8 equal squares. Transfer squares to the prepared baking sheet. Using a sharp knife, score a border about ½ inch from the edge of each square without cutting all the way through.
05 - Spread about 1 tablespoon of cheese filling in the center of each square. Top with a generous spoonful of the cooled apple mixture.
06 - Brush the scored pastry borders with beaten egg to ensure a golden, glossy finish.
07 - Bake for 18–20 minutes until the pastries are puffed and deep golden brown. Transfer to a wire rack.
08 - Allow danishes to cool for 10 minutes. Whisk powdered sugar with milk until a smooth, drizzle-able icing forms. Drizzle over warm danishes and serve.