Preheat the oven to 170°C (338°F).
Sift matcha powder, cake flour, and baking powder together.
Add egg, sugar, milk, and melted butter to a bowl and mix well.
Add the sifted dry ingredients and mix evenly.
Chop the chocolate finely and add it to the batter.
Pour the batter into a cake mold.
Bake in the preheated oven for 25-30 minutes.
Remove from the mold after cooling to complete.