Line a cookie sheet with parchment paper, and set aside.
In a medium bowl, beat cream cheese, powdered sugar, and ½ teaspoon vanilla until smooth and well combined.
Scoop cream cheese using a small cookie scoop (about 2 teaspoons) onto the tray (there should be about 18 scoops). Freeze for 1 hour.
Preheat the oven to 375°F.
Pour the pumpkin onto a plate and blot out all excess moisture until there is no extra moisture. Set aside.
In a medium bowl, mix flour, two teaspoons pumpkin pie spice, baking soda, and salt.
In a large bowl, beat butter on high until smooth. Add brown sugar and ¼ cup white sugar. Beat until combined well.
Pour the pumpkin into the butter and sugar mixture and the remaining vanilla. Beat until mixed well.
Pour the dry ingredients into the wet ingredients and mix with a wooden spoon until combined.
In a small bowl, mix the remaining ¼ cup white sugar and 1 teaspoon pumpkin pie spice.
Scoop pumpkin dough with a medium scoop and pat each ball into a 2½ to 3-inch circle in your palm. Add a frozen ball of cream cheese to the middle, and press the dough around the filling. Roll into a ball and then roll into the sugar and pumpkin pie spice mixture.
Place on the prepared baking sheet and repeat with the remaining dough.
Bake for 12 minutes (Keep remaining dough balls with the cream cheese inside chilled while baking).
Let cool on a baking sheet for 5 minutes before removing to a wire rack to cool completely.