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.
1/2 cup unsalted butter, 1/4 cup dark brown sugar, 1 large egg
Mix in half of the dry ingredients, the molasses, the remaining dry ingredients, and then the buttermilk.
3/4 cup molasses, 1/2 cup 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.