Pre-heat your oven to 180°C. Line two 23cm cake pans with parchment paper.
With an electric mixer, cream together the butter and sugar until it becomes pale yellow in colour. Add the eggs, one at a time, and mix until eggs are well incorporated. Add the vanilla extract.
In a separate bowl, sift matcha powder over the flour - you do not want large clumps of matcha in your cake! Add in the baking powder and salt. Mix well.
Add the bowl of dry ingredients to the bowl of the wet ingredients. Slowly add in the half cup of milk (adjust the amount of milk based on the consistency of the batter). Equally divide the batter between the pans and bake cake for 40 - 45 minutes, checking the doneness of the cake at around 35 minutes. Let the cake cool completely before removing/cutting it.
Once the cakes have completely cooled, cut each equally into half to form four layers in total.
To assemble, place a layer of cake down and smother on a generous portion of the cream cheesing filling. Alternate between the cake layer and cream cheese layers until you have a cake with desired cake and cream cheese layers.
Decorate the cake however you like. I used a combination of matcha meringues, berries and flowers. Before I topped the cake with berries and flowers, I dusted a thin coat of matcha sugar on the top layer of the cake - I thought this made the cake look more presentable. To make the matcha sugar, just sift matcha powder over icing sugar and the amount of matcha depends on what colour you want the matcha sugar to be. You can skip this step if your top layer is a cream cheese layer (versus a naked cake layer).