Preheat the oven to 350 degrees F (175 degrees C). Line the bottom of a 9 inch round cake pan cake pan with parchment paper.
Warm the cream cheese and milk in a small saucepan over medium-low heat. Cook, stirring occasionally, until cream cheese is melted. Remove from the heat and set aside.
In a medium bowl, beat egg yolks and half of the sugar until light and fluffy using an electric mixer. Fold the cream cheese mixture into the yolks. Sift in the flour and cornstarch, and stir until blended.
In a separate bowl, using clean beaters, whip egg whites with cream of tartar until they can hold a soft peak. Gradually sprinkle in the remaining sugar and continue whipping to stiff peaks. Fold egg whites into the cream cheese mixture. Pour into the prepared cake pan. Place the pan on a baking sheet with sides.
Place the baking sheet with the cheesecake into the oven, and pour water into the baking sheet until it is half way full. Bake for 20 minutes in the preheated oven, then reduce the heat to 300 degrees F (150 degrees C). Continue to bake for 15 more minutes. Let the cake cool before removing from the pan.
Run a knife around the outer edge of the cake pan, and invert onto a plate to remove the cake. Peel off the parchment paper and invert onto a serving plate so the top of the cake is on top again.