In a medium nonstick pan over medium heat, add the pumpkin puree. Reduced by half, about 10 minutes, stirring constantly. Be careful not to burnt the puree. Remove from heat and set aside to cool until room temperature, about 30 minutes.
Preheat the oven to 400˚F (200˚C). Arrange racks in lower and upper thirds of the oven. Line 2 baking sheets with parchment papers.
In a stand mixer fitted with a paddle attachment, beat the cream cheese on high speed until fluffy, about 1 minute. Add ½ cup pumpkin puree (not all) and beat until blended. Add ½ cup sugar and beat for 1 minute. Add cinnamon, nutmeg, salt, and vanilla extract. Beat again until combined. Add egg yolk and mix until just blended. Set aside.
On a lightly floured working surface, unfold one puff pastry (keep the other in the fridge) and roll into 12 x 12-inch square with a rolling pin. Cut into 9 squares (4 x 4-inch). Transfer the squares into the 2 baking sheets, and space them apart for about 2 inches.
In a small bowl, beat together 1 large egg and 1 teaspoon water to make egg wash. Set aside.
Scoop about 1 heaping tablespoon cream cheese filling in the center of the puff pastry squares. Brush two opposing corners with egg wash, fold over, overlap the corners a little bit, and pinch tightly to seal.
Brush all of the exposed puff pastry with the egg wash. Sprinkle generously with sugar over the danish.
Bake in the oven 20 – 22 minutes until golden brown, rotating the baking sheets top to bottom and front to back after 10 minutes. Remove from oven and cool for 5 minutes. Transfer to a cooling rack to cool.
Repeat with the second puff pastry sheet.
For the glaze (optional), whisk together powdered sugar and milk in a small bowl. Drizzle the glaze over the danish. Serve warm or at room temperature.