In a stand mixer bowl, combine powdered sugar and matcha powder.
Beat the softened butter into the matcha mixture using a stand mixer, until smooth and light.
Once mixed together, add the flour a little at a time, and the 4 egg yolks, and the salt.
Mix until fully combined, it will be a little sandy in texture.
Stop mixer, and use hands to knead dough a little.
Dump onto a piece of plastic wrap. Don't worry if it is still a little sandy.
Form dough into a disk and wrap in the plastic wrap
Refrigerate for 30 minutes.
Remove dough from plastic wrap, and knead with your hands until it is nice and smooth, and not falling apart. The more you work with it, the less sandy it will be.
Preheat oven to 350 degrees F.
On a smooth, cool surface (like a granite or marble countertop), roll the dough out using a rolling pin, until it is 1 centimeter thick.
Use a small 1-2 inch sized cookie cutter of choice to cut out your shortbread cookies, or a 1 1/2 inch round biscuit cutter.
Place cookies on a parchment lined cookie sheet, and bake for 12-14 minutes, until slightly browned on the bottom.
Remove from baking sheet immediately, and let cool. (Should make 3-4 dozen cookies depending on the size of cookie cutter you use)
Store in an airtight container for up to a week.