Preheat the oven to 350°F (175°C). Grease the inside of a 9″ × 5″ loaf pan (bottom 8″ × 4″).
In a medium bowl, whisk together the eggs, egg yolks, and water. In another bowl, sift together the cake flour, matcha powder, and salt. Set aside.
Place the softened butter in the bowl of a stand mixer and beat with the paddle attachment for 2 minutes. Gradually add the sugar in 4–5 additions, then continue beating for about 5 minutes, until the mixture becomes very light in color and fluffy.
Slowly add the egg mixture in 4–5 additions, mixing over about 5 minutes. Fold in the flour mixture by hand in 4–5 additions until just combined.
Pour the batter into the prepared pan and smooth the surface with a spatula. Bake for about 1 hour, or until done. Let the cake cool slightly, then remove it from the pan. Transfer to a wire rack and cool completely.
