In a medium bowl, add in cream cheese, pumpkin puree, cinnamon, pie spice, brown sugar, and milk. Whisk together until smooth. Set aside.
On a floured surface, unfold one puff pastry and roll out to create a 12-inch square. Using a two-inch circle cookie cutter, cut out 16 circles. Repeat with the extra sheet, and set that aside.
Fill 16 circles with 1 ½ teaspoons of pumpkin mixture. Brush the edges with egg mixture. Top with another circle puff pastry. Pinch the edges together and crimp ends with a fork.
Brush the top of the pastry pies with egg mixture, cut three small slits on top of the pies. Sprinkle with coarse sugar. Place pies onto baking sheets. Bake 20 minutes, or until the pies are golden colored.
Remove from oven and allow to cool for ten minutes.