Beat the egg whites with an electric mixer until stiff peaks form. Set aside. Place the egg yolks and sugar in a bowl and beat until they lighten in colour. Add the vanilla extract and butter and beat until combined. In a separate bowl, combine the flour and matcha green tea powder, then add to the wet mixture and mix until just combined. Gradually add the milk and mix until well combined. Add the beaten egg whites in thirds, folding with a spatula until just combined.
Pour the batter into a buttered 8'x8' square cake pan and bake at 325F for 40-50 minutes, until the cake doesn't jiggle when you gently shake the pan. Cool in the pan for 10 minutes, then remove from the pan and transfer to a wire rack. Cool completely before serving.
To serve, dust the surface with confectioner's sugar and enjoy!