Preheat the oven to 350 degrees and line two baking sheets with parchment paper.
Stir together the flour, baking soda, and pumpkin pie spice in a medium bowl.
In a large bowl, beat the 1/4 cup softened butter with the brown sugar until light. Add the pumpkin puree and egg, then mix until smooth.
Gradually add the dry ingredients to the wet mixture and stir until just combined.
Drop rounded tablespoons of batter onto the prepared sheets, spacing them a few inches apart. Bake for 10 to 12 minutes until the edges look set. Cool completely on a wire rack.
Beat the cream cheese, 2 tablespoons softened butter, powdered sugar, and vanilla extract until creamy.
Spread filling on the flat side of half the cooled cookies and top with the remaining cookies to form sandwiches.