Prep your refrigerator and baking sheets. Make room in your refrigerator for a baking sheet so the shaped cookies can chill. Line two baking sheets with parchment paper or a silicone baking mat. Set aside.
Sift dry ingredients. In a medium-sized mixing bowl, sift the flour, cake flour, salt, and matcha powder and whisk to combine. Set aside.
Cream butter and sugar. In the bowl of a stand mixer fitted with a paddle attachment, cream butter on medium speed until smooth about 1 minute. With the mixer still running on low, slowly add in the sugar. Mix on medium speed until light and fluffy about 3 minutes. Scrape the edges of the bowl to combine.
Incorporate egg yolks, vanilla, and milk. While mixing, add egg yolks, vanilla, and milk. Continue to mix on medium speed until well combined. Scrape down the sides of the bowl to combine.
Combine dry ingredients. Add the dry mixture to the mixer in two parts, and scrape down the sides of the bowl. Mix on low speed until combined and there are no more traces of flour.
Pipe the cookies. Transfer cookie batter to a large piping bag with fitted a ½-inch open star tip. Pipe 2-inch cookies (rosettes, pretzels, circles, squares) on a prepared baking sheet. Space cookies at least 1 inch apart. If desired, sprinkle the dough with festive sprinkles and/or coarse sugar. Chill in the refrigerator for 1 hour.
Prepare the oven. While the cookies are chilling, preheat the oven to 350°F and place the baking rack in the middle of the oven.
Bake. Bake the cookies one tray at a time for 9-11 minutes or until edges are JUST lightly golden brown. Let the cookies cool on the baking sheet for about 5 minutes before transferring to a wire rack to cool to room temperature.