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1
Preheat the oven to 340 degrees F (170 degrees C). Line the bottom of two 9-inch round cake pans with parchment paper.
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2
Mix cake flour, salt, and baking powder thoroughly.
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3
Whisk matcha powder into the hot milk until no lumps remain. Let cool.
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4
Beat yolks in a bowl using an electric mixer; add superfine sugar and blend until dissolved. Whisk in oil until thoroughly combined. Add the matcha-milk mixture and mix well. Sift in 1/4 of the flour mixture at a time, mixing batter well after each addition.
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5
Beat egg whites in a glass, metal, or ceramic bowl until foamy. Add cream of tartar and whisk well. Add 1/4 of the sugar at a time, mixing well after each addition. Continue to whisk until stiff peaks form, or until mixture looks like shaving cream and no bubbles are visible. Do not overmix.
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6
Gently fold 1/3 of the egg white mixture into the yolk batter using a spatula. Repeat with the rest of the egg whites. Pour batter into the prepared cake pans. Chill a clean metal bowl and whisk attachments in the freezer.
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7
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 25 to 30 minutes.
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8
Remove from oven. Invert pans and allow to cool completely; this will prevent the cakes from sinking.
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9
Beat heavy cream and confectioners' sugar together in the chilled metal bowl until soft peaks form. Set frosting aside in the refrigerator.
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10
Beat mascarpone cheese, heavy cream, confectioners' sugar, and matcha powder in another bowl until filling mixture begins to stick to the whisks.
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11
Run a thin knife along the edges of the baking pans to remove the cakes. Spread the mascarpone filling over 1 side of each cake. Place 1 cake on a serving plate, filled-side up; top with the other cake, filled-side down. Spread frosting over the surface.