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 alternately with milk, beginning and ending with confectioners’ sugar, beating just until combined after each addition. Beat in nutmeg and vanilla. Increase mixer speed to medium, and beat until light and fluffy, about 2 minutes, stopping to scrape sides of bowl. Use immediately.