Preheat oven to 340℉/170℃ and line two baking sheets with parchment paper.
Using a hand mixer or stand mixer fitted with a paddle attachment, cream together butter and confectioners' sugar on high speed until pale and fluffy.
Add egg yolk and vanilla. Beat the mixture until well combined.
Sift in cake flour, cornstarch, matcha powdr, and salt. Mix with a spatula until well incorporated. Don't overmix.
Add your star piping tip to the piping bag. Transfer the dough into the piping bag and try piping on the prepared baking sheet. If the dough is too thick to pipe, transfer the dough back to the mixing bowl and add 1 tsp of milk. If the dough is creamy enough to pipe, continue piping the dough into swirls, leaving 2 inches apart on the baking sheet.
Chill in the fridge for at least 30 minutes to let the dough firm up so that they kep their shape better during baking. This step is optional.
Bake cookies for 15-18 minutes or until the edges are light brown. Bake for 15 minutes for softer cookies, bake for 18 minutes for crisper cookies.
Remove from the oven and immediately transfer them to a wire rack to cool completely.
Notes
Make sure to measure the flour correctly if using volume measurement. The cookies will end up too dry if you add too much flour. Use a spoon to scoop the flour into the measuring cup. Then, level the top with a knife or other straight-edged utensil.