In the bowl of a stand mixer fitted with the paddle attachment, beat butter and salt at medium speed until smooth, 2 to 3 minutes, stopping to scrape sides of bowl. With mixer on low speed, gradually add confectioners’ sugar alternately with cream, beating until combined after each addition. Add peppermint extract; increase mixer speed to medium, and beat until fluffy, about 3 minutes. Beat in food coloring until desired shade is reached. Fold in chocolate. Use immediately.