Preheat oven to 325°F, and line the bottom of an 8-inch square pan with parchment paper. Then, lightly spray the exposed sides of the lined pan with cooking spray.

In a medium-size bowl, using an electric mixer on medium speed, beat together the softened butter and sugar until light and fluffy, about 1-2 minutes.

Add the eggs, matcha powder and vanilla, and beat just until combined.

In a small bowl, whisk together the flour and baking powder.

Add half of the flour mixture to the bowl, and stir to combine.

Add all of the buttermilk, and stir again.

Finally, add the remaining half of the flour mixture and stir until no streaks of flour remain, but be careful not to overmix the batter.

Scrape the batter into the prepared pan, and bake on the middle rack for 30-33 minutes, until a toothpick inserted comes out mostly clean with only moist crumbs (not wet batter).

Let the cake cool in the pan for about 15 minutes, until it starts to pull away from the edges of the pan. Then, run a knife around the edge of the cake, and lift it out of the pan and place on a cooling rack to cool completely.

Next, make the frosting: combine all frosting ingredients in a bowl. Then, beat all of the frosting ingredients together until light and fluffy.

Slice the cake in half (from one square into two rectangles), and spread some buttercream on top of one half. Place the opposite cake half on top of the cake half with buttercream.

Decorate the cake with powdered sugar, the remaining buttercream and fresh strawberries. Slice into 5 or 6 triangle slices and serve.