01 - Preheat the oven to 400°F. Line a standard baking sheet with parchment paper.
02 - In a skillet over medium heat, melt the unsalted butter. Add the diced apples, brown sugar, ground cinnamon, ground nutmeg, and fresh lemon juice. Cook for 6 to 8 minutes, stirring frequently, until the apples are tender and the juices become syrupy. Remove from heat and let the mixture cool completely.
03 - In a medium mixing bowl, beat the softened cream cheese, granulated sugar, and pure vanilla extract together until completely smooth and creamy.
04 - Unfold the thawed puff pastry onto a lightly floured work surface, rolling gently to smooth out any creases. Using a sharp knife or pastry wheel, cut the sheet into 8 equal-sized squares.
05 - Transfer the pastry squares to the prepared baking sheet. Using a paring knife, lightly score a smaller square border inside each piece, ensuring you do not cut completely through the dough. Prick the inner center square several times with a fork to prevent excessive puffing.
06 - Divide the cream cheese filling evenly among the centers of the pastry squares. Layer a generous spoonful of the cooled apple mixture directly over the cream cheese, keeping all fillings within the scored inner border.
07 - Using a pastry brush, lightly coat the exposed outer edges of each pastry square with the beaten egg wash to ensure a golden-brown finish.
08 - Bake on the center rack for 18 to 22 minutes, or until the pastry edges are deeply golden and fully puffed. Transfer to a wire cooling rack.
09 - Allow the pastries to cool slightly. In a small bowl, whisk the powdered sugar with milk or lemon juice until a drizzle consistency is reached. Zigzag the glaze over the warm pastries using a spoon, if desired. Serve warm or at room temperature.