Preheat your oven to 350 degrees F. Line a baking sheet with parchment paper or a silicone baking mat.
In a medium mixing bowl, stir together flour, nutmeg, baking powder, baking soda, and salt. Set aside
In a large mixing bowl, beat together butter and sugar until pale and fluffy, 1 to 2 minutes. Add the eggs and mix to combine, scraping the bowl as needed.
Add in half the flour mixture and mix. Add in the eggnog and mix. Then add the remaining flour mixture and mix until just combined.
Portion level cookie scoops of the batter (about 1 tablespoon) into your prepared baking pan, working in batches. You want to leave at least 2-inches between cakes. (I can fit 8 per pan.)
Bake for 10 to 12 minutes, or until the edges of the cakes are a light, golden brown. Remove from the oven and cool in the pan for 5-10 minutes. Then transfer to a wire rack to cool completely.
Buttercream
In a large bowl, beat together butter, powdered sugar, rum, vanilla, and nutmeg until smooth.
Turn half of the cakes upside down. Using a piping bag or a ziptop plastic bag with a corner cut off, pipe a generous amount of frosting onto each upside-down cake. (at least 1 tablespoon)
Place another cake on top, with the bottoms facing each other, and gently press down until the frosting spreads to the edges. Serve immediately or store in an air-tight container.
Notes
I like less frosting on our whoopie pies, so I make half a batch of the buttercream. Traditional whoopie pies have LOTS of frosting. This recipe makes enough buttercream to be generous on your cakes.