Preheat oven to 150°C (300°F). Line a 9x5-inch loaf pan with parchment paper and set aside.

In a small bowl, whisk together the eggs, milk, and vanilla extract until well combined.

In a large mixing bowl, sift the cake flour, matcha powder, salt, and baking powder. Add the sugar and whisk until evenly combined.

Add the softened butter to the flour mixture and beat with a paddle attachment or hand mixer until the mixture becomes light and fluffy. Scrape the bowl to ensure everything is incorporated.

Slowly add the egg mixture in three separate additions, mixing on low speed and scraping the bowl between each. Mix just until smooth.

Pour the batter into the prepared loaf pan and smooth the top.

Bake for 60 to 65 minutes, or until a toothpick inserted into the center comes out clean.

Let the cake cool in the pan for 10 minutes before transferring to a wire rack to cool completely.