Preheat oven to 180°C (160°C fan-forced). Line cupcake tins with cases.
Using a mixer, cream butter, sugar and vanilla until creamy and fluffy. Gradually add eggs and mix until just combined.
Combine flour, cocoa and bicarbonate soda. Add to creamed mixture with milk. Beat until just combined.
Spoon mixture into liners until each case is one-third full. Bake for 15-20 minutes
To make the chocolate butter cream icing, beat butter until light and fluffy. Add icing sugar and cocoa and combine well. Beat in milk until mixture is fluffy.
Once the cupcakes have cooled, cover them with icing and enjoy.