Set up a double boiler: place a heatproof bowl over a pot of gently simmering water. Add the cream cheese and butter. Whisk until completely smooth with no lumps.
Remove the bowl from heat. Whisk in the egg yolks one at a time, then whisk in ⅓ cup sugar, milk, lemon juice, and vanilla extract.
Sift the cake flour, cornstarch, and salt directly into the batter. Fold gently with a spatula until just combined. The batter should be smooth and pourable. Set aside.
Make the Meringue
In a large, clean, dry bowl, beat the egg whites on medium speed until frothy, about 1 minute. Add the cream of tartar.
Gradually add the remaining sugar (about 85g) one tablespoon at a time while beating. Increase to medium-high speed and beat until firm soft peaks form. The meringue should hold its shape but the tip curls over gently when the whisk is lifted. Do not beat to stiff peaks.
Fold and Bake
Scoop about ⅓ of the meringue into the cream cheese batter. Whisk it in to lighten the batter.
Pour the lightened batter into the remaining meringue. Fold gently with a spatula: cut down through the center, sweep across the bottom, fold over the top. Stop as soon as no white streaks remain.
Preheat oven to 400°F (200°C). Line an 8-inch round cake pan (at least 3 inches deep) with parchment paper on the bottom and sides. Lightly grease. Wrap the outside in two layers of foil.
Pour the batter into the pan. Tap gently to release air bubbles. Place inside a larger roasting pan. Pour hot water into the roasting pan until it reaches 1 inch up the sides of the cake pan.
Bake at 400°F (200°C) for 15 minutes. Reduce to 300°F (150°C) and bake 40 to 50 minutes more until the top is golden and the center has a slight jiggle.
Cool and Serve
Turn off the oven and keep the door closed for 20 minutes. Then crack the door open about 2 inches (prop with a wooden spoon) and leave for 30 more minutes.
Remove from oven and water bath. Cool on a wire rack to room temperature, about 1 hour.
Refrigerate for at least 2 hours before serving. Run a thin knife around the edges and lift out using the parchment paper overhang. Slice and serve chilled or at room temperature.
Notes
Soft peaks, not stiff: Over-beaten meringue is the top cause of cracking. Stop when the tip curls over gently.
Room temperature everything: Cold cream cheese creates lumps. Cold eggs won't whip properly. Pull ingredients out at least 1 hour ahead.
Water bath is essential: Wrap your pan in foil to keep water out. The steam provides gentle heat and prevents cracking.
Some shrinkage is normal: Expect the cake to settle about ½ inch as it cools. This is not a failure.
Cake flour substitute: Use all-purpose flour if needed, but the texture will be slightly denser.
Cream of tartar substitute: Use ½ teaspoon lemon juice or white vinegar.
Storage: Refrigerate wrapped for 3-4 days. Freeze wrapped in plastic and foil for up to 3 months.