Preheat the oven to 300°F (150°C). Grease and line an 8-inch springform pan with parchment paper and wrap the outside with foil if it is a loose-bottom pan.
Place the prepared pan in a larger baking tray and pour about 1/2 inch of hot water into the tray to create a water bath; set aside.
In a small saucepan over low heat, melt the cream cheese, unsalted butter, and whole milk, stirring until smooth; remove from heat and let cool slightly.
Sift together the cake flour, cornstarch, and salt into a bowl.
In a large bowl, whisk the warm cream cheese mixture with the egg yolks, 2 teaspoons lemon juice, vanilla extract, and half of the granulated sugar (about 6 tablespoons) until smooth. Gradually stir in the sifted dry ingredients until fully combined.
In a clean bowl, beat the egg whites on low speed until foamy. Gradually add the remaining sugar, then increase speed and beat until soft peaks form.
Fold one-third of the whipped egg whites into the batter to lighten it, then gently fold in the remaining egg whites in two additions, preserving as much air as possible and mixing until just combined.
Pour the batter into the prepared pan, smooth the top, then place the pan into the water bath and transfer to the oven. Bake at 300°F (150°C) for 30 minutes with the oven door closed.
After 30 minutes, bake for 20 minutes with the oven door slightly open, then bake another 20 minutes with the door closed (total about 70 minutes). The cake should have a golden top and a slight jiggle.
Remove from the oven and let cool in the pan for 15 minutes, then gently release from the springform and cool completely on a rack. Serve slightly warm or chilled.