Preheat the oven to 350 degrees F and line a baking sheet with parchment paper.
In a medium bowl, whisk together the flour, baking soda, cinnamon, nutmeg, ginger, and salt.
In a separate bowl, mix the pumpkin puree, brown sugar, vegetable oil, and egg until smooth.
Combine the wet and dry mixtures until a thick batter forms.
Drop 8 rounded tablespoons of batter onto the baking sheet, spacing them apart, and bake for 12 minutes until the edges are set.
Cool the cookies completely on a wire rack.
Beat the cream cheese, powdered sugar, and vanilla until smooth to make the filling.
Spread filling on the flat side of four cookies and top each with a second cookie to form the whoopie pies.