Make the pies:
Preheat oven to 350 F. Line 2 baking sheets with parchment paper.
In a large bowl, whisk together the flour, cinnamon, pumpkin pie spice, baking soda and salt; set aside.
In a large bowl, with an electric mixer, beat the brown sugar, granulated sugar, oil and pumpkin on medium speed until well-combined, about 1 minute. Beat in the eggs one at a time, beating well after each addition; stir in the vanilla. Gradually beat in the flour mixture on low speed until just combined.
Transfer the mixture to a large piping bag or zip-top plastic bag fitted with a medium round tip. Pipe the batter in 2-inch circles 2 inches apart on the prepared baking sheets.
Bake in the preheated oven for 11 minutes, or until the tops are set, rotating the baking sheets halfway through baking time. Let cool on baking sheets for 5 minutes, then transfer to a wire rack to cool completely, about 30 minutes.
Make the cream cheese filling:
In a large bowl, with an electric mixer, beat the cream cheese and butter on medium speed until smooth.
Gradually beat in the powdered sugar on low speed until smooth, about 1 minute. Stir in the cinnamon and vanilla.
Assemble:
Place the filling in a large piping bag or zip-top bag fitted with a medium round tip.
Pipe the filling on to the flat side of half of the cookies. Top the filling with another cookie to create whoopie pies.
Serve immediately or chill overnight. Store in the refrigerator up to 4 days.
