Preheat oven to 320°F (160°C). Grease and line a 9-inch round cake pan with parchment paper, extending the paper above the edges.
In a double boiler or heatproof bowl set over simmering water, combine cream cheese and sugar. Stir until smooth and creamy.
Remove from heat and whisk in egg yolks one at a time, then stir in milk, melted butter, and vanilla extract.
Sift in flour and cornstarch, and whisk until just combined.
In a separate clean bowl, beat egg whites and cream of tartar until stiff peaks form.
Gently fold the egg whites into the cream cheese mixture in three additions, being careful not to deflate the egg whites.
Pour batter into the prepared pan. Place the cake pan in a larger pan and add hot water to the larger pan to create a water bath (about 1 inch deep).
Bake for 50-60 minutes, or until the top is golden brown and the cheesecake is set but still slightly wobbly.
Turn off the oven and let the cheesecake cool in the oven with the door ajar for 1 hour.
Remove from the oven and water bath, and let cool completely on a wire rack. Refrigerate for at least 4 hours before serving.