In a small saucepan, bring cream and corn syrup to a boil. Remove from heat, and whisk in white chocolate until melted. Allow to cool completely in pan.
In the bowl of an electric mixer, using the paddle attachment, cream the butter on medium-high speed until somewhat fluffy. On low speed, add cooled chocolate mixture and blend well.
Add confectioners’ sugar and peppermint extract. Blend well until all sugar is incorporated.
Remove buttercream and place in a bowl. Use immediately or store in the refrigerator, covered, for up to 1 week. Allow refrigerated buttercream to come to room temperature before using.