In a pan melt together the butter and chocolate. Stir till smooth. Let it cool to room temperature.
Pour the cooled butter and chocolate mixture in the steel bowl of your stand mixer fitted with paddle attachment.
With mixer at slow speed, start adding the sugar. Once the sugar is incorporated, increase the mixer speed to high and beat for 30 seconds. Repeat the process with the remaining sugar. Also add the vanilla.
Mix heavy cream/milk and beat at high speed for 1 minutes till smooth and creamy.