Preheat oven to 350 degrees.
In a medium sized mixing bowl or stand mixer, mix together sugar, cake flour, baking powder, baking soda, and salt.
Add butter and mix on medium-low speed for about three minutes.
In a small mixing bowl, whisk together eggs, yogurt, oil, and vanilla extract until smooth.
Slowly add milk and mix on low speed until just combined.
Bake for 16 minutes and then test to see if they are done by inserting a toothpick into the center. If it comes out clean, they are done. If not, bake for another 1-2 minutes and check again.
When the cupcakes are done, transfer them to a cooling rack and wait until they cool before icing them.
Mix matcha powder into vanilla icing. If you have a pastry bag, pipe the icing onto the cupcakes, otherwise use an icing knife or regular knife to spread icing.