Preheat the oven to 175°C (350F) and line a large baking sheet with parchment paper (you may need to line 2 baking sheets or make these in 2 rounds).
Sift and mix dry ingredients (flour, matcha, baking soda, cream of tartar, salt) in a large bowl and set aside.
Place softened cubed butter and sugar in a large bowl of a stand mixer fitted with the paddle attachment. Mix on medium speed until mixture is pale and fluffy (1-2 minutes). Use a spatula to scrape any ingredients from the side of the bowl.
Add vanilla extract, egg, and egg yolk and mix for 2 minutes until well-combined.
Add dry ingredients and mix until just combined and cookie dough forms. Do not overmix.
Using a cookie scoop or your hands, grab around 40g (1.4oz) of cookie dough and roll into a ball. Repeat for the remaining cookie dough.
Roll each cookie dough ball into some sugar and transfer to baking sheet, leaving a 2 inch space between each one.
Bake in the oven for 11-13 minutes, or until the edges start to turn slightly golden brown. Cookies will be soft when out of the oven and will harden as they cool.
If you'd like flat, wrinkly cookies, carefully lift the baking sheet (be careful as it would be hot), then bang down on a heat-proof surface a few times, to force cookies to breathe out all their hot air and flatten. Allow to cool slightly, then transfer to a wire rack to cool completely.