Preheat oven to 350°F. Line two baking sheets with parchment.
Whisk flour, pumpkin pie spice, baking powder, baking soda, and salt in a bowl.
Beat softened butter with brown sugar and granulated sugar until fluffy, about 2 minutes.
Mix in pumpkin puree and 1 teaspoon vanilla until smooth and creamy.
Add dry ingredients in two additions, alternating with buttermilk. Stir just until combined.
Scoop 2-tablespoon mounds onto sheets, spacing 2 inches apart. Smooth tops if needed.
Bake 12–14 minutes until set and springy. Cool on sheets 5 minutes, then on racks.
Beat cream cheese and 1/4 cup butter until silky. Add powdered sugar, 1 1/4 teaspoons vanilla, salt, and cinnamon; beat until thick and spreadable.
Pair similar-sized cakes. Spread or pipe filling on one half and cap with its mate.
Chill assembled whoopie pies 15 minutes to help the filling set before serving.