Preheat the oven to 175 degrees Celsius. Whisk together flour, baking powder, salt and green tea powder in a bowl. Set it aside.
Beat butter and sugar together until pale and creamy, for 3 minutes on high speed, scraping the sides occasionally. Beat in the egg until fully incorporated and then add in the egg yolk, beating until fully incorporated.
Fold in the flour mixture in three parts, alternating with the milk, beginning and ending with the flour mixture. Divide the batter into 12 cupcakes cup and bake for 22 to 25 minutes until the cupcake has risen and a skewer inserted into the centre of the cake comes out clean.
Let the cupcakes cool completely on a wire rack before frosting them.
Frosting
Warm the milk and dissolve the green tea powder. Let cool completely.
Beat the butter with an electric mixer until soft and fluffy. Beat in the green tea mixture. Continue beating and add in the icing sugar, until the frosting reaches your desired consistency and sweetness.