In a small saucepan, gently heat the milk, heavy cream, and 5 tablespoons of sugar over low heat until dissolved, about 5 minutes. Cool to room temperature.

In a blender, combine the cooled cream mixture with eggs, vegetable oil, cake flour, and matcha powder. Blend until smooth, about 30 seconds.

Sift the batter into mixing bowls and cover with plastic wrap. Let rest in the fridge for at least 1 hour or overnight.

Check the batter consistency and add water until it's thin and pourable.

Heat a non-stick skillet; add a small pat of butter. Pour in about 1/4 cup of batter, swirling to cover the pan. Cook for 2-3 minutes, flip, then cook for another minute. Transfer to a cooling rack.

Chill a mixing bowl and beaters for 10 minutes. Add heavy cream and powdered sugar; beat until stiff peaks form, about 2-3 minutes.

Layer the crepe: place one on a dish, spread a thin layer of whipped cream, repeat until all crepes are used.

Cover the cake and refrigerate for at least 4 hours, preferably overnight, to meld flavors.

Dust the top with matcha powder before serving; slice into 8 pieces and enjoy.