How to Make It
Heat the oven to 350°F. Butter two 8-inch round cake pans and line the bottom of each with a round of parchment paper.
Combine the flour, baking powder, salt, and matcha powder in a medium bowl. Using an electric mixer, beat the butter in a large bowl until soft. Add the sugar and continue mixing until light and fluffy, 2-3 minutes. Add the eggs one at a time, mixing to combine. Stir in the vanilla. Add the matcha mixture and the milk in increments, alternating between them. Stir until just combined. Divide the batter evenly between the two prepared cake pans.
Bake cakes for 25-30 minutes, until a toothpick inserted in the center comes out clean. Let rest for 15 minutes, then remove from pans and transfer to a wire rack to cool completely before frosting.
Make the frosting: Using an electric mixer, beat the butter on high until light and fluffy, 3 to 5 minutes. Reduce mixer speed to low. Gradually add the sugar, then the vanilla and salt, and beat until smooth.
Assemble the cake: Using a small serrated knife, carefully trim the sides of both of the cakes, removing any browned or golden bits, so that only green is visible. Transfer one cake to a cake stand or platter and spread with ¾ cup frosting. Top with the remaining cake, making sure the flat side is facing up. Cover the entire cake with a thin layer of frosting, dragging a spatula or a butter knife against the sides to scrape away the frosting in places. Finish the top with a thick layer of frosting. Serve cake at room temperature. (It is best the day it is made.)