Preheat your oven to 350°F (175°C) and line a muffin tin with cupcake liners.
In a large bowl, beat the softened butter and sugar until light and fluffy. Add the eggs one at a time, beating well after each addition with an electric mixer at high speed.
Whisk together the flour, baking powder (not baking soda), and matcha powder in a separate bowl.
Gradually add the dry ingredients to the butter mixture, alternating with the milk, until everything is combined.
Divide the cupcake batter evenly among the muffin cups, filling each about ⅔ full.
Bake for 20 minutes or until a toothpick inserted into the center of a cupcake comes out clean.
Let the cupcakes cool in the muffin cup for a few minutes, then transfer them to a wire rack to cool completely.
Once cooled, you can decorate the cupcakes with a frosting of your choice, such as a cream cheese frosting, whipped cream frosting, or buttercream frosting (this is what I used). Enjoy your delicious and flavorful matcha cupcakes!