Gather your baking sheets and line them with parchment paper. Shape the cookie dough into rounds and place them on the sheets. Chill for at least 1 hour.

Sift together all-purpose flour, cake flour, salt, and matcha powder in a medium bowl. Break up clumps of matcha.

In a stand mixer, combine room-temperature butter and granulated sugar. Beat on medium speed for about 3 minutes until light and fluffy.

Reduce mixer speed to low and add egg yolks, vanilla extract, and whole milk. Mix until well combined.

Gradually introduce the dry mixture into the wet ingredients, mixing gently until no traces of flour remain.

Transfer dough to a piping bag fitted with a round tip. Pipe 2-inch shapes onto the baking sheets. Preheat oven to 350°F and bake for 9-11 minutes.