Preheat your oven to 350°F (175°C) and grease a 9-inch round cake pan.
In a medium bowl, whisk together the flour and matcha powder until well combined.
In a large bowl, cream together the butter and sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition.
Slowly add the flour mixture to the wet ingredients, alternating with the milk, beginning and ending with the flour.
Stir in the vanilla extract until just combined.
Pour the batter into the prepared cake pan and smooth the top.
Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.