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For the cupcakes:
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1. Preheat oven to 350 F. Line two 12-count standard size muffin or cupcake tins with paper liners. Set aside.
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2. In the bowl of your stand mixer with paddle attachment, cream butter at medium speed until soft, about 30 seconds.
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3. Add sugar. Beat on medium-high until light and fluffy, about 2 minutes.
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4. Add eggs and egg yolks one at a time, beating well between addition. Beat in vanilla.
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5. Whisk together flour, baking powder, and salt in another smaller bowl.
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6. Mix matcha with the milk in another small bowl.
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7. Add a third of the flour mixture to the batter. Mix well. Follow by a third of the milk mixture. Mix well. Continue alternating dry and wet ingredients until everything is well incorporated.
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8. Scoop batter evenly into prepared cupcake papers.
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9. Bake for 22-25 minutes until a cake tester inserted in the center of one comes out clean. Remove from oven and let cupcakes cool before frosting.
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For the frosting:
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1. In a small bowl or cup, mix matcha with the milk to make a paste.
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2. In a mixing bowl with an electric mixer, beat butter briefly.
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3. Add the sifted powdered sugar and matcha paste. Beat until smooth. Then blend in the vanilla.
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To assemble:
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1. Pipe or spread about 2 tablespoons of the matcha frosting onto each cupcake. Serve!