Preheat your oven to 320°F (160°C). Line the bottom of a 9-inch round cake pan with parchment paper and grease the sides.
In a heatproof bowl, melt the cream cheese, butter, and milk over a double boiler. Stir until smooth, then remove from heat.
Sift together the flour, cornstarch, and salt. Gradually add this mixture to the cream cheese mixture, stirring constantly until well combined.
Beat in the egg yolks one at a time, ensuring each yolk is fully incorporated before adding the next. Add the vanilla extract and lemon juice, mixing until smooth.
In a clean, dry bowl, whip the egg whites until soft peaks form. When you lift the whisk out of the egg whites, the peaks should gently fold over.
While still whipping the egg whites, gradually add the granulated sugar. Continue whipping until stiff peaks form and the texture is smooth and glossy. This might take a few minutes, and it's crucial for the texture of your Japanese cheesecake.
Use a spatula to carefully scoop 1/3 portion of the whipped egg whites and gently fold it into the cream cheese batter with a whisk. Repeat this process 2 more times, until all the whipped egg whites are incorporated. Remember to fold gently to maintain the light and airy texture of the cheesecake.If you whisk the white eggs and fold it correctly correctly, you will see that the mixture almost does not decrease in volume. It is very fluffy and smooth, with almost no air bubbles. Pour the batter into the prepared cake pan and smooth the top with a spatula.
Place the cake pan in a larger baking pan. Add hot water to the larger pan, ensuring it covers about 1/3 to 1/2 of the height of the pan, creating a water bath for the cheesecake.
Bake in the preheated oven for about 1 hour and 15 minutes. Once the cake achieves a golden color (around 40-50 minutes), quickly open the oven door. Cover the top with foil, perforated to prevent steaming. Continue baking for 60-65 minutes until the surface is puffy and rounded.The cake is ready when the surface appears puffy and rounded. To check doneness, gently press the surface—it should bounce back. Allow the cheesecake to cool in the oven with the door ajar for about 20 minutes Then, refrigerate for about 4 hours or overnight before serving.