Preheat the oven to 160°C (320°F). Line the bottom and sides of an 8 or 9-inch round pan with parchment. Wrap the outside of the pan with foil to prevent water entering during the water bath.

In a heatproof bowl over simmering water or in a microwave in short bursts, combine the cream cheese, butter, and milk until smooth and warm to the touch. Whisk in vanilla, lemon juice, and a pinch of salt.

Sift the cake flour and cornstarch into the warm cream cheese mixture. Add the egg yolks one at a time, stirring until smooth. The batter should be silky and slightly thick.

In a clean bowl, beat the egg whites with cream of tartar until frothy. Gradually add the sugar while beating, until you reach stiff, glossy peaks.

Fold one third of the meringue into the yolk batter to lighten it. Gently fold in the remaining meringue in two additions, preserving as much air as possible.

Pour batter into the prepared pan and smooth the top. Tap gently to remove large air bubbles. Place the pan in a larger roasting pan and pour hot water into the outer pan until it reaches halfway up the cake pan. Bake for 55 to 65 minutes, until the top is light golden and the center jiggles slightly when gently shaken.

Turn the oven off and leave the door closed for 10 to 15 minutes. Remove the cake from the oven, take it out of the water bath, and let it cool on a rack. Invert the cake to cool upside down, propping it with a chopstick.

Chill in the refrigerator for at least 2 hours before serving for clean slices. Slice with a hot, dry knife for neat pieces.