Mix together cake mix, egg, canola oil, water and peppermint extract until smooth. Pipe into a greased mini donut pan. Bake at 350 degrees for 7-10 minutes. Keep an eye on them. You may need to take them out sooner or keep them in longer.
While donuts are baking, mix together powdered sugar, melted butter and milk. I like to start with 2 tablespoons of milk and add more until I reach my desired consistency.
Crush 4-5 candy canes. Dip cooled mini donuts in icing and then in the crushed candy canes.