Preheat oven to 180°C/160°C. Grease two 12-hole, 1 tablespoon-capacity mini muffin pans.
Using an electric mixer, beat butter, vanilla and sugar in a small bowl until light and fluffy. Add eggs, 1 at a time, beating after each addition (mixture will separate at this stage). Transfer mixture to a large bowl. Stir in half the flour and cocoa. Stir in half the milk. Repeat with remaining flour, cocoa and milk until combined.
For 1/3 cup-capacity muffin pans use 2 level tablespoons of mixture. Bake for 15 to 17 minutes. Alternatively, for 1 tablespoon-capacity mini muffin pans use 1 tablespoon mixture. Bake for 10 to 12 minutes.
Stand cakes in pans for 2 minutes. Transfer to a wire rack to cool.
Make icing: Using an electric mixer, beat butter until light and fluffy. Gradually beat in icing sugar until smooth. Beat in coffee essence. Spoon mixture into a snap-lock bag. Snip a 1cm triangle from 1 corner of bag. Pipe mixture over cakes. Decorate with sprinkles. Serve.
