Preheat oven to 375 °F (191 °C). Line baking sheets with parchment paper or silicone baking mats. Set aside.
In a large bowl, whisk together all the dry ingredients.
In the bowl of a stand mixer (or using a hand mixer), beat butter and brown sugar together until light and fluffy. Beat in the egg, scraping down the sides of the bowl.
Mix in half of the dry ingredients, the molasses, the remaining dry ingredients, and then the buttermilk.
Drop the batter onto baking sheets using a medium cookie scoop (or 1 1/2 tbsp.).
Bake the cakes until puffed and set, about 9-12 minutes. Cool on the baking sheets until firm then transfer to a wire cooling rack to cool completely.
In the meantime, in a clean bowl of a stand mixer (or using a hand mixer), beat the butter and cream cheese together. Carefully add the powdered sugar until incorporated, then add the vanilla extract, lemon zest, and juice of 1 lemon. If the frosting is too runny, add more powdered sugar, 1/4 cup at a time. If the frosting is too stiff, add a tbsp. of milk at a time until desired consistency.
To assemble whoopie pies, spread a heaping tablespoonful of filling onto the flat side of half the cakes then top with the second, unfilled cake, rounded side up.