If you are using candy canes or peppermint candies, place them in a bag and crush them with something heavy like a rolling pin. To get smaller pieces, you can also grind the candy in a small grinder or food processor (see notes).
Make a boxed cake batter as directed adding in the peppermint extract as well. Fold in the peppermint candy. Bake the cake and allow it cake to cool completely.
Once the cake has cooled, break it into pieces and place them into a large mixing bowl. Break up the pieces with a spatula or spoon to get small crumbles.
Take the container of frosting and mix ¾ of it into the crumble mixture (you can use the whole can, but it's not necessary). The mixture will be between a batter and a dough.
Prepare a cookie sheet with a silicone mat or wax paper. Scoop out about 1 tablespoon of cake mixture and roll it into a ball between your hands. Place each ball on the wax paper and continue to make balls with the rest of the mixture.
Place the cookie sheet in the freezer while preparing the candy coating (this step is optional but I feel like it makes the dipping process a little easier).
Melt the candy coating in a microwave-safe bowl in the microwave according to the directions on the package. This will take about 2 minutes. Do not overcook the coating or it will burn.
Add 2-3 tablespoons of vegetable oil (or coconut oil) to the candy coating to thin it out for dipping.
Dip each ball into the melted coating and cover it completely. Tap off the excess coating and place the ball back on the wax paper. Immediately top the ball with crushed peppermint candy pieces so they stick before coating sets.
Allow the balls to set completely before enjoying them. You can speed up the process in the fridge, or if it's a really warm day, you should put them in the fridge so they are set.