Preheat your oven to a warm 350°F (175°C). Lightly grease and flour two 9-inch round cake pans, ensuring an easy release.
In a large mixing bowl, combine the dry cake mix, water, large eggs, your chosen oil (or applesauce), and the peppermint syrup. Mix gently until just combined and smooth; avoid overmixing for a tender cake.
Evenly pour the vibrant batter into your prepared cake pans.
Bake for 20-25 minutes, or until a thin toothpick inserted into the cake's center comes out perfectly clean. Let the cakes cool completely on a wire rack before moving on.
For the delightful frosting, combine the softened butter, powdered sugar, an initial 3 tablespoons of milk (or water), and pure peppermint extract in a large bowl. Using an electric mixer, beat on medium speed until the frosting is light, fluffy, and perfectly blended. Only add the additional tablespoon of milk if you need a thinner consistency.
Once your cakes are cool, generously spread the creamy peppermint frosting over and between the layers.
For that festive finishing touch, gently press the crushed peppermint candy cane pieces onto the sides and top of the cake. Slice and serve this easy, holiday-ready treat!