Preheat oven to 350°F/177°C.
In a clean stand mixer bowl fitted with a whisk attachment, add in the egg whites and gradually whip until foamy.
Add in cream of tartar or lemon juice and continue to increase the speed until more bubbles form.
Gradually add in the granulated sugar until stiff peaks form. Set aside.
In a bowl, whisk together the egg yolks, milk, vanilla, and matcha. Sift in the all-purpose flour, baking powder and sea salt.
Use a spatula to fold in the dry ingredients, until just combined.
Fold in ⅓rd of the egg white mixture into the egg yolk-flour batter to lighten.
Continue to fold in the rest of the whipped egg whites into the flour batter, until incorporated.
Transfer the cake batter to a square 8" by 8" baking tray.
Lightly tap to release any trapped air bubbles.
Bake at 350°F/177°C for 20-25 minutes, until the surface of the cake is dry to the touch and springs back when lightly pressed.
Let the cake cool for 10-15 minutes before poking with a skewer.