In the bowl of a stand mixer fitted with the paddle attachment, beat butter and salt at medium speed until creamy, about 1 minute, stopping to scrape sides of bowl. With mixer on low speed, gradually add confectioners’ sugar, about 1 cup (120 grams) at a time, alternately with cream, about 1 tablespoon (15 grams) at a time, beginning and ending with confectioners’ sugar, beating just until combined after each addition. Increase mixer speed to medium; beat until fluffy, 1 to 2 minutes. Fold in chocolate. Use immediately.