Preheat your oven to 390°F and lightly grease a 8” x 3” round cake pan with butter. Line the bottom with parchment paper.
Pour boiling water into a large bowl or pan, then sit a smaller mixing bowl inside. Add the cream cheese to the smaller bowl and let soften while you separate your eggs. When the cream cheese is soft, whisk until smooth and creamy, then stir in butter and milk until smooth and incorporated. Whisk in the yolks until smooth, then whisk in the sugar. Remove the bowl from the hot water bath and sift in the cake flour and cornstarch. Whisk until smooth.
Whip the egg whites with the cream of tartar until frothy and pale, adding sugar bit at a time until the whites are whipped into a glossy thick meringue that holds a soft peak. Be careful not to over whip.
Take 1/3 of the whipped egg whites and whisk it into the bowl with the yolks until completely incorporated. Add half of the remaining whites and whisk into the yolk batter, being careful not to deflate.
Transfer the egg yolk mixture to the remaining egg whites, whisk and then use a spatula to fold together. Pour the batter into the prepared cake pan – it should come up almost to the top of the pan, about 1/4 inch from the top. Tap the pan against the counter to release any air bubbles.
Place a kitchen towel into a large deep baking dish and place the cake pan on top (this ensures that the cheesecake doesn’t have any contact with direct heat), then put everything into the preheated oven and carefully pour hot water about 1 inch high.
Bake at 390°F for 18 minutes, then drop the heat to 285°F and bake for another 30 minutes. When the 30 minutes is up, turn off the oven and leave the cake inside without opening the door for another 30 minutes. Finally, open the oven door and remove the water bath. Place the cake back into the oven and leave the door slightly open to let cool gently for another 30 minutes. The idea is to let the cake cool very gradually so it doesn’t crack.
The cake will have naturally shrunk from the sides and should be cool enough to touch. Use a cutting board (or your hands) to invert and remove from the pan. Flip back right side up and place on your serving dish. It should be soft, fluffy, and jiggly while it’s still warm.