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Preheat your oven to 325°F. Grease and flour a 9x5-inch loaf pan (or a Bundt pan if you're feeling fancy). Sift the matcha powder with the flour, baking powder, and salt. Set aside.
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In a large bowl, cream the butter and sugar together with an electric mixer on medium speed for 4-5 minutes until light and fluffy. This step matters — don't rush it.
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Add the eggs one at a time, beating well after each addition. Scrape down the sides of the bowl between eggs. Mix in the vanilla.
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With the mixer on low, add the flour mixture in three additions, alternating with the milk in two additions (flour, milk, flour, milk, flour). Mix just until each addition is incorporated.
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Pour the batter into the prepared pan and smooth the top. Tap the pan gently on the counter to release any air bubbles.
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Bake for 55-65 minutes until a toothpick inserted in the center comes out clean. The cake should be golden around the edges with a beautiful green crumb inside.
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Let it cool in the pan for 15 minutes, then turn it out onto a wire rack to cool completely. Dust with powdered sugar or drizzle with a simple glaze if you like.