Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.
In a medium-sized bowl, sift together the flour, baking powder, baking soda, salt, and pumpkin pie spice.
In a large bowl, combine the pumpkin purée, brown sugar, egg, and vanilla extract. Whisk until smooth.
Gradually stir in the dry ingredients into the pumpkin mixture until just combined.
Using a medium ice cream scoop, drop about 1½ to 2 tablespoons of batter onto the prepared baking sheets.
Spread the dough into about a 2-inch diameter round.
Bake for 15 minutes, switching the baking sheets halfway through.
After baking, let them cool on the baking pans for about 10 minutes.
Peel the cookies from the parchment and allow them to cool completely on racks.
In a large mixing bowl, beat together the butter and cream cheese until creamy.
Add the confectioners' sugar and vanilla extract. Mix until fluffy.
Turn half of the cookies over and pipe in the filling, then top with the other half.
