Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a large bowl, cream together the butter and sugar until light and fluffy.
Beat in the eggs one at a time, mixing well after each addition.
In a separate bowl, sift together the flour, baking powder, salt, and matcha powder.
Gradually add the dry ingredients to the wet ingredients, alternating with the milk. Mix until just combined.
Stir in the vanilla extract.
Pour the batter into the prepared cake pan and smooth the top.
Bake in the preheated oven for 30-35 minutes or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
Slice and serve the matcha green tea cake.