Preheat the oven to 300 degrees F. Spray a 9-inch round cake pan with cooking spray and line the bottom with parchment. Place a 3 1/2-inch-wide strip of parchment around the inside of the pan so that it comes up about 1 inch higher than the edge; set aside.
Heat the cream cheese, milk and butter in a small saucepan over medium heat, whisking occasionally, until smooth. Remove from the heat and let cool slightly, about 5 minutes.
Whisk together the vanilla, egg yolks and lemon juice in a large bowl until smooth. Pour the cooled milk mixture into the yolk mixture and whisk until smooth and combined. Whisk in the flour and cornstarch until combined; set aside.
Beat the egg whites, cream of tartar and 1/2 teaspoon salt in a large bowl with an electric mixer on medium speed until soft peaks form, about 2 minutes. Slowly add the granulated sugar and continue beating on medium speed until stiff peaks form, about 2 minutes longer.
Gently fold the egg white mixture into the yolk mixture in 3 batches, making sure not to overmix (you want the whites to stay as fluffy as possible). As soon as the white streaks disappear from the batter, pour it into the prepared pan.
Place the cake pan inside of a larger pan and pour enough hot water into the larger pan so that it comes 1 inch up the sides of the cake pan. Bake for 30 minutes, then reduce the oven to 250 degrees F and continue baking until the cake is doubled in size, golden brown on top and around the edges and jiggly in the center but set, about 1 hour and 15 minutes.
Let the cake cool for 10 minutes. Carefully invert the cake onto your dominant hand (right onto your palm--this is the most gentle way to handle it), then invert it back onto a cake stand or plate so that the top is facing up. Sprinkle the entire top with confectioners' sugar and serve while still warm.
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