In a mixing bowl, mix the softened butter and sugar with a spoon until a smooth paste. Mix in the egg yolks, milk, and vanilla extract until fully incorporated. Add the flour, sifted matcha powder, salt, and baking powder, and mix until a thick dough forms.
½ cup butter, ⅔ cup granulated sugar, 2 egg yolks, ⅓ cup milk, 1 tsp vanilla extract, 1 cup cake flour or all-purpose flour, 2 tsp matcha powder, ¼ tsp salt, ½ tsp baking powder