Preheat the oven to 325F (160C).
Grease a non-stick bundt pan, ensuring to get into all of the creases. Then dust with flour. Or brush with pan release/cake goop.
Whisk the egg whites until frothy, then add in ¼ granulated sugar and continue whisking until stiff peaks form. Set aside.
In a medium bowl, sift together the flour, nutmeg, baking powder and salt. Whisk until evenly combined.
In a large bowl, beat the butter, 1 cup granulated sugar and ¾ cup brown sugar until fluffy.
Mix in the oil, egg yolks, vanilla extract and rum (or rum extract).
Sift in about ½ of the flour mixture into the butter mixture. Whisk in until smooth.
Whisk in about ½ of the eggnog.
Sift in the rest of the flour mixture, and whisk in. Then whisk in the rest of the eggnog until the mixture is smooth. Stop mixing as soon as the mixture is smooth.
Pour the batter into the prepared pan. Bake in the preheated oven for 60-70 minutes, or until an inserted toothpick comes out clean and you see the edges starting to pull away from the pan.
Cool in the pan for 15-30 minutes, then gently invert onto a wire rack to continue cooling.