Remove the top layer of cream from the chilled coconut milk. Place in the bowl of an electric mixer and beat on medium speed until soft peaks form, about 5 minutes. Beat in confectioner's sugar gradually until well combined, about 2 minutes. Add yogurt, coconut butter, vanilla extract, and salt; beat for 1 minute more. Transfer to an airtight container and chill in the refrigerator until firm, about 4 hours.