Preheat oven to 350F and grease and flour three 6" cake rounds, line with parchment.
In a medium bowl, whisk flour, baking powder, nutmeg, cinnamon, and salt. Set aside.
Using a stand mixer fitted with the paddle attachment, beat butter until smooth. Add sugars and beat on med-high until pale and fluffy (2-3mins).
Reduce speed and add eggs one at a time, fully incorporating after each addition. Add vanilla.
Alternate adding flour mixture and eggnog, beginning and ending with flour (3 additions of flour and 2 of eggnog). Fully incorporating after each addition. Do not overmix.
Spread batter evenly into prepared pans. Smooth the tops with a spatula.
Bake for approx. 30-35mins or until a toothpick inserted into the center comes out mostly clean.
Place cakes on wire rack to cool for 10mins then turn out onto wire rack. Poke holes into the warm cakes and brush with some of the cooled rum simple syrup to moisten them***. Allow cakes to cool completely.
Rum Simple Syrup:
Place sugar and water into a small saucepan and cook over high heat until simmering and sugar is dissolved. Remove from heat and stir in rum. Allow to cool slightly before using on cake.
Cream Cheese Frosting:
Beat butter and cream cheese until fluffy (2 mins). Add powdered sugar one cup at a time. Add vanilla & nutmeg and beat until fluffy (3 mins).
White Chocolate Ganache:
Place chopped chocolate and cream (or eggnog) into a microwave safe bowl. Stir to combine. Microwave for 20 seconds, stir. Microwave in 10 second intervals, stirring in between, until smooth and silky. Set aside to cool and thicken slightly before using on cake.
Place one layer of cake on a cake stand or serving plate. Top with 2/3 cup of frosting. Repeat with remaining layers and apply a thin coat of frosting all over the cake. Use a bench scraper to smooth the sides. Chill for 20mins.
Using a teaspoon, drip ganache along the edges then fill in the top and smooth. Chill for 15mins. Sprinkle with nutmeg and top with rosettes if desired I used a 1M tip.
* I forgot to include the nutmeg in my frosting but had intended to have it in there!
** If the ganache is too thick (mine was a bit), add in a tsp of heavy cream until it gets to a thin enough consistency.
*** You will have some rum simple syrup leftover. You can use this to sweeten/spike cocktails or hot beverages like coffee or hot chocolate.