Preheat oven to 350F, grease three 6" round baking pans and dust with cocoa powder. Line bottoms with parchment.
Place all dry ingredients into the bowl of a stand mixer fitted with a paddle attachment. Stir to combine.
In a medium bowl whisk all wet ingredients (pour water in slowly as not to cook the eggs if very hot).
Add wet ingredients to dry and mix on medium for 2-3 mins. Batter will be very thin.
Pour evenly into prepared pans. I used a kitchen scale to ensure the batter is evenly distributed.
Bake until a cake tester comes out mostly clean. A total of 30-35mins.
Cool 10 minutes in the pans then turn out onto a wire rack to cool completely.
Peppermint Swiss Meringue Buttercream:
Place egg whites and sugar into the bowl of a stand mixer, whisk until combined.*
Place bowl over a hot water bath on the stove and whisk constantly until the mixture is hot and no longer grainy to the touch (approx. 3mins). Or registers 160F on a candy thermometer.
Place bowl on your stand mixer and whisk on med-high until the meringue is stiff and cooled (the bowl is no longer warm to the touch (approx. 5-10mins)).
Switch to paddle attachment. Slowly add cubed butter and mix until smooth.**
Add vanilla and peppermint extract (to taste) and whip until smooth.
Remove 1 1/2 cups of buttercream (more if doing inside stripes). To that add 2-3 Tbsp of powdered sugar and enough color gel to achieve the red you want. Color will darken slightly over time.
If desired, whiten the remaining frosting to remove the yellow tint by using bright white color gel or following these tips.
Place one layer of cake on a cake stand or serving plate. Top with about 2/3 cup buttercream. Sprinkle with 1/4 cup crushed candy canes if desired. Repeat with remaining layers. Frost and smooth the outside with a thin crumb coat. Chill for 20mins.
Frost and smooth the outside of the cake, generously frosting the sides specifically. Smooth with an icing smoother. Use a cake comb on the sides of the cake. Repeat, scraping off more frosting each time, until smooth.
Pipe dollops of the red buttercream on top, slightly separated, using a 1M piping tip. Pipe smaller dollops of the white frosting in between the red ones using a 4B tip. Decorate the bottom with crushed candy canes and sprinkles if desired.
* Ensure there is NO trace of egg yolks in your whites and that your mixer bowl and whisk is completely grease-free or your meringue won't stiffen.** The buttercream may look like it's curdled at some point. Keep mixing until it is completely smooth.