Heat milk and chocolate until melted and combined, cool to room temperature.*
Preheat oven to 350F. Grease and flour two 8" cake rounds and line with parchment.
In a medium bowl, whisk flour, baking powder, and salt until well combined. Set aside.
Using a stand mixer fitted with a paddle attachment, cream butter and sugar on med-high until pale and fluffy (approx 3mins). Reduce speed and add eggs one at a time fully incorporating after each addition. Add peppermint extract.
Alternate adding flour mixture and milk mixture, beginning and ending with flour (3 additions of flour and 2 of milk). Fully incorporating after each addition.
Bake for 45-50mins 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 and cool completely.
White Chocolate Swiss Meringue Buttercream:
Place egg whites and sugar into the bowl of a stand mixer, whisk until combined.**
Place bowl over a double boiler 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 white chocolate, vanilla (or more peppermint extract) and whip until smooth.
Candy Cane Bark:
Melt red and white candy melts in bowls over simmering pots of water.
Using a large offset spatula, spread white candy melts in a thin, even layer on a large sheet of parchment.
Pour melted red candy melts into a piping bag. Snip off the tip to about 1/2" in size. Pipe diagonal strips across the sheet of white. Spread using a small offset spatula to flatten.
Roll up from the short side of the parchment. Place on a baking sheet and refrigerate or freeze until firm (approx. 30mins in fridge).
Remove 1/3 of the frosting and color it red. You'll need to use a fair amount of color gel to do this. Frosting will darken a bit over time.
Fill one piping bag, fitted with a large round tip with the red frosting, fill another with the white.
Place one layer of cake on a cake stand or serving plate. Alternate piping white and red circles starting from the outside edge working your way in.
Place second cake layer on top and repeat the same process.
Apply a thin coat of the white frosting on the outside of the cake. Smooth the sides and top. Leave a bit of the sides exposed for a naked look if desired. Chill for 20mins.
Place remaining red and white frosting in a separate piping bag fitted with a French piping tip. I used a spatula to spread the white on one side of the piping bag and the red on the other. Pipe rosettes on the top of the cake.
Fill the middle between the rosettes with chopped candy canes and white chocolate shavings if desired.
Place candy cane bark around the outside of the cake. Adhere with some extra buttercream if needed.
* You can do this in the microwave, stirring between 30 second bursts or in a pot in the stove, stirring constantly, or in a double boiler, stirring occasionally. ** 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.