Preheat oven to 170C/325F/(gas mark 3) and line a 12 cup muffin pan with paper cases.
Tear the cavolo nero leaves into bite sized pieces and boil or steam them for a few minutes until tender. Refresh by running under cold water to cool, then drain, squeeze out any excess moisture, chop up very finely.
Add the kale and milk to a tall container, then puree until smooth with a hand blender.
In a large bowl, cream the butter and sugar with an electric mixer until light and fluffy. Beat in the eggs, one at a time, then beat in pureed cavolo nero.
Sift in the flour and stir gently to combine.
Fill the muffin cups ¾ full with the batter and bake for 15-20 minutes or until a skewer inserted in the middle comes out clean. Allow to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
For the frosting
Beat the butter with an electric mixer until light and fluffy, then sift in the icing sugar and cocoa and add the milk and vanilla and beat until smooth. If the frosting is too thick, add another tablespoon of milk. If it’s too thin, add a little powdered sugar, sparingly, until it reaches a thick frosting consistency.
Spoon the frosting into a piping bag and pipe over the cooled cupcakes.