Prepare the Batter

1. Preheat the Oven: Set your oven to 325°F (160°C). Line the bottom of an 8-inch round cake pan with parchment paper and grease the sides.
2. Melt the Ingredients: In a heatproof bowl over a double boiler, combine the cream cheese, butter, and milk. Stir until smooth. Remove from heat and let it cool slightly.
3. Incorporate the Yolks: Whisk the egg yolks and vanilla extract into the cooled mixture until fully combined.
4. Sift and Fold: Sift in the cake flour, cornstarch, and matcha powder. Gently whisk until there are no lumps.

Make the Meringue

5. Beat the Egg Whites: In a clean mixing bowl, beat the egg whites on medium speed until foamy.
6. Add Sugar Gradually: Slowly add the sugar and lemon juice, continuing to beat until stiff peaks form. The meringue should hold its shape when the whisk is lifted.

Combine and Bake

7. Fold the Meringue: Carefully fold the meringue into the matcha batter in three additions. Use a spatula and gentle motions to keep as much air as possible in the mixture.
8. Prepare a Water Bath: Pour the batter into the prepared cake pan. Place the pan inside a larger baking dish and fill the outer dish with about 1 inch of hot water.
9. Bake: Bake at 325°F (160°C) for 60 minutes, then turn off the oven and let the cake sit inside with the door slightly open for another 10 minutes.
10. Cool: Remove the cake from the oven, let it cool in the pan for 15 minutes, then gently remove it from the pan.