Preheat your oven to 350°F (175°C) and grease an 8-inch cake pan or a 9 x 5 x 3-inch loaf pan, lining the bottom with parchment paper for easy removal. I highly recommend weighing the dry ingredients in grams rather than scooping them into your measuring cup, as using too much flour will result in too dense of a matcha cake.
In a large bowl, sift together the flour, matcha powder, baking powder, and salt to ensure there are no lumps and everything is well incorporated.
In a separate bowl, whisk together the eggs and sugar until the mixture is pale and slightly thickened.
Slowly pour in the butter and vanilla extract into the sweet egg mixture, continuing to whisk until everything is well combined.
Gradually add the dry ingredients to the wet ingredients, alternating adding the flour mixture with adding the milk. Start and end with the dry ingredients, mixing until just combined after each addition. Be careful not to overmix, as this can lead to a dense cake.
Pour the batter into the prepared cake pan and smooth out the top with a spatula.
Bake for 45-50 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for about 10 minutes before transferring it to a wire rack to cool completely.