Preheat oven to 350°F (175°C). Grease and flour a 9x5 inch loaf pan.
In a medium bowl, whisk together flour, sugar, baking powder, and salt.
In a large bowl, cream together the softened butter and sugar until light and fluffy.
Beat in the eggs one at a time, then stir in the matcha powder.
Gradually add the dry ingredients to the wet ingredients, alternating with the milk, beginning and ending with the dry ingredients. Mix until just combined.
Pour batter into the prepared loaf pan and bake for 50-60 minutes, or until a wooden skewer inserted into the center comes out clean.
Let cool in the pan for 10 minutes before transferring to a wire rack to cool completely.
Notes
For a richer flavor, use full-fat milk and high-quality matcha powder. Store leftover cake in an airtight container at room temperature for up to 3 days.