Preheat your oven to 350°F (175°C). Grease and flour a 9x5-inch loaf pan.
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large mixing bowl, cream the softened butter and granulated sugar together until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, mixing well after each addition. Then, add the matcha powder and vanilla extract, mixing until combined.
Gradually add the dry ingredients to the wet mixture, alternating with the whole milk. Start and end with the flour mixture, mixing until just combined.
Pour the batter into the prepared loaf pan and smooth the top. Bake for 50-60 minutes, or until a toothpick inserted in the center comes out clean.
Allow the cake to cool in the pan for 10 minutes, then transfer it to a wire rack to cool completely.