In a heatproof bowl placed over a saucepan of simmering water, melt chocolate, not letting the bottom of the bowl touch the water. Remove from heat, and let cool to room temperature.
In a stand mixer fitted with the whisk attachment, beat butter until smooth and creamy, approximately 1 minute. Add sugar, and beat until light and fluffy, approximately 2 minutes. Beat in vanilla extract and then chocolate at low speed until incorporated. Increase speed to medium-high and beat until frosting is smooth and glossy, 2 to 3 minutes.
Recipe by TeaTime Magazine at https://teatimemagazine.com/indulge-delectable-delights-intrigue-baker-street-mysteries-return-murder-piece-of-cake/