Combine the oil and brown sugar. Mix in the pumpkin and eggs, beating well. Add the flour, salt, baking powder, baking soda, vanilla, cinnamon and nutmeg. Mix well.
Drop dough by heaping teaspoons onto the prepared baking sheets. Bake at 350 degrees F for 10 to 12 minutes. Let cookies cool then make sandwiches from two cookies filled with cream cheese icing.
Make the filling: In the bowl of an electric mixer with the paddle attachment, beat room temperature butter until smooth. Add room temperature cream cheese and beat until well combined. Add confectioners’ sugar, vanilla and cinnamon, beat just until smooth. Cover and refrigerate; let stand at room temperature to soften before using.
Add the icing to form little whoopie pie “sandwiches.” Serve and enjoy! Refrigerate any leftovers.