Preheat oven to 350°F and coat all three pans with non-stick spray.
Whisk together the milk and peppermint extract in a small bowl and set aside.
In the bowl of a stand mixer, cream together butter and sugar until light and fluffy.
In another large mixing bowl, whisk together the flour and baking powder.
Alternate pouring milk and dry ingredients into the stand mixer bowl of butter and sugar, mixing on medium speed.
Rinse out one of the mixing bowls and use it to beat the egg whites until stiff peaks form. Fold egg whites into the cake batter.
Divide the cake batter evenly between 2 mixing bowls. Leave one bowl of batter white. Add 3-5 drops of red food coloring to the second bowl of batter and mix until the batter is a rich red. Add more food coloring as needed.
Scoop one cup each of white batter and one cup of red batter into each of the three cake pans. Use a butter knife to gently swirl the batter together.
Bake cakes for 23-26 minutes, or until a toothpick inserted in the middle comes out clean.
Allow the cakes to cool completely before removing from cake pans and onto a cutting board.
Using a cake slicer or our cake cutting trick to level the three cakes.
To Make the Frosting:
Use a standing mixer to beat all ingredients together until stiff peaks form.
Scoop about a cup of the frosting into a piping bag and set aside.
To Assemble the Cake:
Place one layer of cake onto a cake board or cake stand.
Scoop a cup of frosting onto the first layer and smooth with an offset spatula.
Repeat with remaining layers of cake, making sure to thoroughly coat the entire cake with frosting once all three layers are stacked.
Gently press crushed candy canes onto the sides of the cake, until fully coated. Take your frosting bag and pipe dollops of frosting on top of the cake. Finish with remaining crushed candy canes.
Note: Nutrition information is a rough estimate only; actual values will vary based on the exact ingredients used and amount of recipe prepared.