Preheat the oven to 350ºF. Lay out 12 cupcake cases on a baking tray.
Beat the eggs with a fork in a separate bowl. Mix the butter, sugar, flour and cocoa powder in a bowl. Using an electric mixer, add the beaten eggs slowly into the bowl as you are mixing.
Using a large spoon place equal amounts of mixture into the 12 cupcake cases. Put the cupcakes into the oven (near the top) and bake for 15 to 20 minutes.
Check on them after 15 minutes, they should be firm to touch. (You can also test by popping a skewer into the middle of the cupcake, it should come out clean). If not ready, leave them in for a further five minutes. Remove from the oven and leave to cool.
While the cupcakes are cooling, make the buttercream topping. Place the butter into a bowl and stir in the icing sugar and vanilla extract using a wooden spoon. Then whisk (again using an electric mixer) until fluffy and lighter in colour.
Add two teaspoons of milk and whisk again. If the mixture is still too stiff add a little more milk.
Once the cakes have cooled completely, put the buttercream mixture into a piping bag with a large star nozzle and squeeze plenty of buttercream onto each cupcake.