Preheat the oven to 300F/150C. Prepare the 8-inch cake pan by lining the pan with parchment paper. If using a springform pan, wrap the pan in foil for the water bath.
In a saucepan over medium-low heat, whisk together the cream cheese, butter, and milk until melted and smooth.
Remove from heat and add the egg yolks, ¼ cup sugar, lemon juice, and vanilla extract. Whisk until even and just combined. Try not to overmix.
Sift in the cake flour, cornstarch, and salt and whisk until combined.
In a separate bowl, make the meringue by beating the egg whites until they begin to foam. Add the cream of tartar and the remaining ¼ cup sugar and whip to soft peaks.
Gently fold the meringue into the batter, mixing until just combined.
Add the batter to the prepared 8-inch cake pan. Place the 8-inch pan into the larger pan. Fill the larger pan with hot water up to halfway up the 8-inch pan.
Bake at 300F/150C for 25 minutes. Decrease the heat to 275F/135C and continue to bake for an additional 55 minutes or until the top is lightly golden and the center still vibrates lightly when jostled.
Turn off the oven, leaving the cake inside. Open the door to the oven slightly to allow hot air to escape. Leave the cake in the oven for an additional 20 minutes, allowing it to cool slowly, which prevents the soufflé from collapsing or cracking.