Preheat the oven to 170°C (338°F).
In a bowl, add eggs and sugar and whip until the mixture becomes pale.
In another bowl, sift the matcha powder, cake flour, and baking powder together.
Melt the butter and milk using a double boiler or microwave.
Add the dry ingredients to the whipped eggs and mix.
Add the melted butter and milk, and mix until combined.
Pour the batter into the mold and bake in the preheated oven at 170°C (338°F) for 25-30 minutes.
Cool on a wire rack to finish.