Preheat oven to 350* F. Grease an 8x8 inch square baking pan and line it with a parchment paper sling.
In a medium bowl, combine the flour, baking powder and salt. Whisk to combine.
In a large bowl, combine the sugar and matcha. Whisk until no lumps of matcha remain. Then, add the non-dairy milk, melted vegan butter and vanilla. Whisk well.
Add the dry ingredient into the wet ingredients and whisk to form the batter.
Scrape the batter into a prepared 8x8 inch pan and use a rubber spatula to spread the cake into the corners of the pan.
Bake in a 350* oven for 32-35 minutes or until a toothpick inserted into the center of the cake comes out clean. Allow to cool completely before frosting.
In a large bowl with a hand mixer, cream the vegan butter until completely smooth. Add the powdered sugar and mix on low until combined. Then add the vanilla and non-dairy milk and mix on medium speed until light and fluffy, about 1-2 minutes.
Remove the cake from the pan. Use a spoon to dollop frosting onto the cake, then use the back of the spoon to spread the frosting.
Slice and serve.
