Place one layer of cake onto a serving plate. Place all of the yellow buttercream on top and spread out into an even layer. Add another layer of cake, then repeat the process with the purple buttercream. Add another layer, top with the white buttercream, then add the final layer.
Use an offset spatula to smooth out any icing that has squished out from the filling. Smooth a thin layer of pink icing all over the top and sides of the cake, to act as a crumb coat (see Note 3). Put the cake into the fridge for about 15 minutes, to allow the buttercream to firm up before proceeding.
When the crumb coat has set, use the remaining pink icing to generously ice the top and sides of the cake, using an offset spatula to smooth it out as much as you can (see Note 4).
At this point, you'll want to remove your chocolate nest from the fridge. Carefully peel the baking paper off the bottom, then set the nest on top of the cake, making sure to centre it. Once you have added the nest, put the whole cake back into the fridge for a further 15 minutes, to firm up the final buttercream layer.
When the buttercream has chilled for 15 minutes, mix together the cocoa powder and vanilla extract in a small bowl. Remove the cake from the fridge, then dip the pastry brush into the cocoa mixture. Use your finger to pull back the bristles and flick the mixture towards the cake to make little chocolate speckles, reminiscent of a Mini Egg.
The cocoa mixture will set relatively quickly, so you can move onto adding the Mini Eggs. Place a row of the eggs all around the base of the cake, then pile the remaining eggs into the chocolate nest on top of the cake.
The cake can be served immediately, or left at room temperature until you are ready to eat it. As always, cake is best eaten on the day it is made, but it will last for about 2-3 days if necessary.