Be sure to allow the butter and the eggnog to come up to room temperature before using. The rum simple syrup can be made ahead of time and stored in the fridge until needed. Make your own eggnog by following this easy eggnog recipe. It will add amazing flavor to this cake. !
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In the bowl of your mixer, beat together butter, oil, and sugar until pale and fluffy (2-3 minutes). Scrape down sides of bowl and add eggs, one at a time, beating thoroughly before each addition. Stir in vanilla extract.
Gradually alternate adding the dry mixture and the eggnog to the butter/egg mixture (3 flour additions, 2 eggnog additions), mixing only until just combined. After all ingredients have been added, stir batter a few more times with a wooden spoon or spatula.
Beat butter, spices, and vanilla until light and fluffy. With the beaters running on low, gradually powdered sugar and 3 tablespoons of eggnog. Increase mixer speed to high and beat frosting until airy, about 5 minutes. If frosting is still too stiff, add the additional tablespoon of eggnog.