Preheat oven to 350 degrees. Line three 6-inch cake pans with parchment rounds, then coat with baking spray. Set aside.
In a large bowl, combine all dry ingredients and whisk until blended. With a spoon, create a well in the middle.
Add eggs, eggnog, vegetable oil, and vanilla and stir until combined. Scrape down the sides of the bowl and add the boiling water. Whisk until well combined.
Divide batter evenly between the three cake pans and bake for 30-35 minutes, or until a toothpick inserted comes out clean, with only a few crumbs.
Allow cakes to cool in pans for 5 minutes, then remove to cooling rack to cool completely.
In a medium saucepan, whisk together sugar, flour, and nutmeg until well blended. Place saucepan on stove over medium heat and, while whisking, add in eggnog. Whisk until no lumps remain.
Continue to whisk until mixture comes to a low boil and thickens enough to coat the back of a spoon. Remove from heat and cool for 45 minutes-1 hour.
In a stand mixer fitted with a whisk attachment, or with a hand mixer, beat butter for 3-5 minutes until pale and creamy. Pour in cooled eggnog mixture ¼ cup at a time, mixing well between additions, until light and creamy. (Don't stress if it looks a bit curdled - just give it a few more minutes and it will come together.)
When it's almost ready, add rum and vanilla and whip until incorporated. Reserve ¾ cup buttercream in a pastry bag.
Using a sharp serrated knife, carefully slice any domed tops off of each cooled cake layer, then slice each layer in half horizontally. Place a layer on a cake board or plate and, using an offset spatula, fill and spread 1/4 to 1/3 cup buttercream to cover layer. Repeat with remaining layers, then chill for 30 minutes in the fridge.
Use the remaining buttercream to cover the top and outside of the cake. Garnish bottom half with chocolate sprinkles, then store cake in fridge until ready to serve.
In a small saucepan, bring heavy cream to a bare simmer over medium heat. Place chocolate chips in a bowl, then pour hot cream over. Allow to sit 4-5 minutes, then whisk from the middle outward until chips are melted and blended, and ganache is dark brown and shiny.
Allow to cool 15 minutes, then remove cake from fridge. Pour desired amount of ganache on top of cake and, using an offset spatula, spread it to the edges and allow to drip down the sides.
Top cake off with dollops of reserved buttercream and additional chocolate sprinkles. Enjoy!