Preheat the oven to 350°F and line a small loaf pan or 6-inch round pan with parchment paper.
In a mixing bowl, whisk together the flour, granulated sugar, 1½ tablespoons matcha powder, baking powder, and salt until evenly combined.
Add the ¼ cup softened butter, egg, milk, and vanilla extract to the dry mixture. Stir until a smooth batter forms with no large lumps.
Pour the batter into the prepared pan and smooth the top. Bake for 22-25 minutes until a toothpick inserted in the center comes out clean.
Cool the cake completely in the pan before removing it.
In a small bowl, beat together the powdered sugar, 1 tablespoon softened butter, and 1 teaspoon matcha powder until a thick frosting forms. Spread the frosting over the cooled cake.
Press candy eyes onto the frosting to finish.