Prepare red bean filling, if making yourself. In essence, boil the beans until soft, then drain and blend or press through a sieve. Nami wrote much more detailed instructions for red bean paste in this blog post.
Preheat oven to 350 F. Grease and line two 7" round cake pans. (For a 3-layered cake as pictured, you can also bake 3 thinner layers in 3 pans.)
With your mixer combine oil, sugar and eggs until light and creamy. Add and mix in other cake ingredients.
Pour batter into cake pans and bake for about 30 minutes. Cool cake layers for 10 min. in pans, then invert onto wire racks and let cool fully.
Whip softened butter with whisk attachment of your mixer until creamy and lighter in colour. Sift in icing sugar and optional matcha powder and combine. Add milk and whip for another 5 minutes on high speed.
Place first cake layer onto a serving plate. Spread a thin layer of buttercream on top and pipe a dam of buttercream around the edge. Spoon red bean paste on the inside of the dam to the thickness of your liking. Place other cake layer on top. (Repeat previous steps if making 3-layered cake).
Ice top and sides of the cake with remaining buttercream. You can dust a little more matcha powder onto the top as decoration.