Preheat your oven to 350°F (175°C). Prepare two 9-inch round cake pans by greasing and lightly flouring them or using parchment paper.

In a bowl, combine the flour, baking powder, salt, and 2 tablespoons of matcha powder. Whisk them together until well mixed.

In a separate large bowl, cream the softened butter and granulated sugar until light and fluffy, about 3-5 minutes.

Incorporate the eggs one at a time, mixing well after each addition. Then add vanilla extract and mix until fully blended.

Gradually add the dry ingredient mixture to the wet ingredients, alternating with the milk. Begin and end with the dry ingredients, mixing just until incorporated.

Pour the batter evenly into the prepared cake pans. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.

Allow the cakes to cool in the pans for 10 minutes before transferring them to a wire rack to cool completely.

In a mixing bowl, beat the softened butter until creamy. Gradually add powdered sugar and 2 tablespoons of milk. Mix until smooth. Add the 1 tablespoon of matcha powder and blend until combined.

Once the cakes are completely cooled, place one layer on a plate. Spread an even layer of frosting over the top, place the second layer on top, and frost the entire cake.