Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
In a large bowl, cream butter, brown sugar, and granulated sugar until light and fluffy.
Beat in pumpkin puree, egg, and vanilla until well combined.
In a separate bowl, whisk together flour, oats, baking soda, baking powder, cinnamon, ginger, nutmeg, and salt.
Gradually add dry ingredients to wet mixture until just combined.
Scoop tablespoonfuls of dough onto prepared baking sheets, spacing about 2 inches apart.
Bake for 12–14 minutes, until cookies are set and lightly golden. Cool completely on wire racks.
Meanwhile, prepare filling: Beat butter and cream cheese until smooth. Gradually mix in powdered sugar and vanilla until fluffy.
Spread or pipe cream filling onto the flat side of half the cookies. Top with remaining cookies to form sandwiches.
Chill for 30 minutes before serving for best texture.