Preheat the oven to 180°C/fan 160°C/gas mark 4. Line 2 cupcake tins with 16 small paper cases.
Place the butter and caster sugar in a bowl and beat using a handheld electric mixer until the mixture is pale and fluffy. Add the eggs, flour and cocoa powder and continue to beat for a few minutes more.
Add enough milk to make the mixture a soft, dropping consistency, then use it to half fill the cases. Place a piece of white chocolate in the centre of each cake, then top with the remaining mixture. Bake in the oven for 15-20 minutes until well risen and firm to the touch. Allow to cool completely.
Meanwhile, put the butter and 2 tbsp water in a small saucepan and heat gently until the butter melts. Remove from the heat and add the icing sugar and cocoa powder. Beat with a wooden spoon until smooth. While the frosting is warm, spread a little on top of each cake and decorate with mini eggs.