Preheat your oven to 400°F (200°C). Line a large baking sheet with parchment paper or a silicone baking mat to prevent sticking and ensure even browning.
In a medium mixing bowl, beat the softened cream cheese and granulated sugar together until smooth. Add the pumpkin puree, vanilla extract, and pumpkin pie spice. Mix until the color is uniform and the texture is creamy.
Unroll the cold puff pastry onto a lightly floured surface. Cut the sheet into 8 equal rectangles or squares. Place the pieces onto your prepared baking sheet, leaving about two inches of space between each one.
Using a sharp knife, lightly score a smaller rectangle inside each pastry piece, about half an inch from the edge. Do not cut all the way through. This creates a “border” that will puff up around the filling.
Place a generous tablespoon of the pumpkin cream cheese mixture into the center of each pastry square. Spread it slightly to fill the inner scored area. Brush the exposed borders of the pastry with the beaten egg wash.
Bake for 15 to 18 minutes, or until the pastry borders are puffed and deep golden brown. Remove from the oven and let them cool on the pan for at least 10 minutes.
Whisk together the powdered sugar and milk until smooth. Once the danishes have cooled slightly, drizzle the glaze over the top in a zig-zag pattern. Serve warm or at room temperature.