Preheat the Oven:
Preheat your oven to 325°F (165°C). Grease an 8×8-inch baking pan with butter and set aside.
Prepare the Eggnog:
Warm the eggnog in the microwave for about 1-1 ¼ minutes in 15-second increments until lukewarm.
Whip the Egg Whites:
In a bowl, combine the room temperature egg whites and vinegar. Using a mixer on high speed, whip until stiff peaks form. Set aside. The vinegar helps stabilize the peaks, which is important for success, especially at high altitude.
Mix the Egg Yolks and Sugar:
In a second bowl, beat the egg yolks and confectioners’ sugar until well combined and pale yellow. Gradually add the melted butter and mix on low speed until fully incorporated.
Add the Dry Ingredients:
Slowly add the flour to the batter, mixing on low speed until well blended.
Incorporate the Eggnog Mixture:
Combine the rum (or additional eggnog) and vanilla with the warmed eggnog. With the mixer on low speed, slowly pour the eggnog mixture into the batter. The batter will be very liquid, which is normal.
Fold in the Egg Whites:
Gently fold the egg whites into the batter one fourth at a time. The batter will remain fairly liquid with small lumps of egg whites.
Bake:
Pour the batter into the prepared pan and bake in the preheated oven for 50-55 minutes. The top will turn golden, but the cake may still jiggle slightly when done.
Cool:
Let the cake cool completely on a wire rack (about 3 hours), or cool for 30 minutes, cover with foil, and refrigerate for at least an hour.
Serve:
Sprinkle the top with confectioners’ sugar and freshly grated nutmeg before serving.