Preheat the oven to 350°F (175°C) and line two baking sheets with parchment paper.
In a bowl, whisk together flour, salt, baking soda, baking powder, and Pumpkin Pie Spice; set aside.
In a separate large bowl, whisk together granulated sugar, brown sugar, and vegetable oil until well combined.
Mix in the pumpkin puree until smooth, then whisk in eggs and vanilla until fully incorporated.
Gradually add the dry ingredients to the pumpkin mixture, whisking until no flour streaks remain.
Scoop the dough onto the prepared baking sheets. Bake each sheet one at a time for 10-12 minutes.
Allow cookies to cool on the sheet for 10 minutes, then transfer to a wire rack to cool completely.
For the filling, beat butter and cream cheese in a bowl until smooth. Add powdered sugar, maple syrup, and vanilla; beat until smooth.
To assemble, turn half of the cookies upside down and pipe the cream cheese filling onto the flat side.
Top with another cookie, pressing down slightly to spread the filling.
Chill assembled whoopie pies in the refrigerator for at least one hour before serving.