FOR BUTTERCREAM: In a large bowl, beat butter until creamy. Gradually add in confectioner’s sugar one cup at a time, scraping down sides of bowl as necessary. Add milk until you reach desired consistency. Add peppermint extract and mix well.
If desired, place icing in piping bag fitted with a large round tip and frost cupcakes, or just frost as desired. You can also use a ziploc bag with the corner snipped off if you don't have a piping bag.