In the bowl of a stand mixer fitted with the paddle attachment, beat butter and brown sugar at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Beat in egg until well combined. Beat in molasses until well combined.
In a medium bowl, whisk together flour, ginger, cinnamon, baking soda, baking powder, salt, and nutmeg. With mixer on low speed, gradually add flour mixture to butter mixture, beating just until combined. Cover and refrigerate for 1 hour.
Preheat oven to 350°F (180°C). Line baking sheets with parchment paper.
In a shallow bowl, place granulated sugar. Using a 1/-tablespoon spring-loaded scoop, scoop dough (about 30 grams each), and roll into balls. Roll in granulated sugar. Place 2 inches apart on prepared pans.
Bake until bottoms are golden and tops are set,10 to 15 minutes. Let cool on pans for 5 minutes. Remove from pans, and let cool completely on wire racks.
Place Eggnog Buttercream in a pastry bag fitted with a 1/3-inch closed star piping tip (Ateco #844). Pipe buttercream onto flat side of half of cookies. Place remaining cookies, flat side down, on top of buttercream. Refrigerate until buttercream is set, about 30 minutes. Store in an airtight container for up to 3 days.