Combine egg and butter in a large bowl. Mix until combined. Pour in devil’s food cake and mix until the batter is smooth (about 2 min). Roll dough into a ball and push flat onto a lined cookie sheet. Bake at 350 for 6-8 minutes. Remove to cooling rack and allow cookies to completely cool.
For frosting: Mix together butter. Next add milk, vanilla and peppermint extract. Then slowly add powdered sugar and beat until fluffy.
Frost one cookie on the BOTTOM and then sandwich another cookie on top. I like to use a lot of frosting (make sure it’s coming out the sides). Then dip the sides of the cookie into crushed peppermint andis.