Preheat oven to 177 °C (175 °C). Grease and flour a 9-inch round cake pan, or line the bottom with parchment paper and grease the sides.

In a medium bowl, whisk together flour, granulated sugar, matcha powder, baking powder, and salt. Ensure the matcha is well distributed to avoid clumps.

In a large bowl, cream together softened butter and vanilla bean paste until smooth. Beat in eggs one at a time until fully incorporated.

Gradually add the dry ingredients to the wet ingredients, alternating with the buttermilk. Begin and end with the dry ingredients, mixing until just combined. Do not overmix.

Pour the batter into the prepared cake pan and spread evenly. Bake for 28-35 minutes, or until a toothpick inserted into the center comes out clean.

Let the cake cool in the pan for 10-15 minutes before inverting it onto a wire rack to cool completely.

While the cake cools, prepare the frosting. In a large bowl, beat the softened butter until creamy. Gradually add the sifted powdered sugar, alternating with the heavy cream and vanilla bean paste, until the frosting is light and fluffy.

Once the cake is completely cool, carefully slice it horizontally into two equal layers.

Place the bottom cake layer on your serving plate. Spread a generous amount of frosting over the top. Carefully place the second cake layer on top.

Frost the top and sides of the cake with the remaining frosting. Garnish with fresh berries, if desired.