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 teaspoon vanilla extract, 1 cup cake flour or all-purpose flour, 2 teaspoon matcha powder, ¼ teaspoon salt, ½ teaspoon baking powder