Preheat the oven to 350°F (175°C).
In a bowl, whisk together the flour, baking soda, baking powder, ginger, cinnamon, cloves, and salt.
In another large bowl, cream the softened butter, brown sugar, and granulated sugar until light and fluffy.
Add the egg, molasses, and vanilla extract to the butter mixture, mixing until well combined.
Gradually incorporate the dry ingredients into the wet mixture, stirring until just combined.
Drop rounded tablespoons of the batter onto lined baking sheets, leaving space between them.
Bake for 10-12 minutes, or until the edges are set, and the cookies spring back lightly when touched.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack.
While the cookies cool, prepare the cream cheese filling by beating together the cream cheese, powdered sugar, and vanilla until smooth.
Match the cooled cookies by size and spread the cream cheese filling on one cookie, topping with another to create a sandwich.
Chill the assembled whoopie pies in the refrigerator for at least 30 minutes before serving.