Preheat oven to 350 degrees F (175 degrees C). Grease 2 12-cup ladyfinger cake pans or canoe pans.
Cream butter and white sugar in a bowl with an electric mixer until fluffy; mix in eggs and 1 teaspoon vanilla extract. Whisk flour, baking powder, and 1/4 teaspoon salt in a separate bowl; gradually mix flour mixture into butter mixture, a little at a time, alternating with milk to make a smooth batter. Spoon batter into prepared cake pans.
Bake in the preheated oven until the snack cakes are golden brown and set in the middle, about 20 minutes. Let snack cakes cool about 10 minutes before turning out to finish cooling on wire racks.
Dissolve 1/4 teaspoon of salt in hot water in a small bowl and set aside. Mix marshmallow creme, vegetable shortening, confectioners' sugar, and 1 teaspoon vanilla extract in a separate bowl. Beat with an electric mixer on high until filling is fluffy. Beat the salt solution into the filling. Pipe filling into cooled snack cakes.
