**Preheat the Oven:**

Preheat your oven to 320°F (160°C). Line the bottom and sides of your cake pan with parchment paper.

**Melt and Mix:**

In a double boiler, melt the cream cheese, butter, and milk, stirring until smooth. Remove from heat and let cool.

**Mix Dry Ingredients:**

Sift together the cake flour, cornstarch, and salt in a bowl. Set aside.

**Combine Wet Ingredients:**

Once the cream cheese mixture has cooled slightly, add the egg yolks and vanilla extract, whisking until smooth. Gradually fold in the dry ingredients until just combined.

**Beat Egg Whites:**

In a clean bowl, beat the egg whites with cream of tartar until frothy. Gradually add the sugar and continue beating until stiff peaks form.

**Fold the Mixtures:**

Gently fold the beaten egg whites into the cream cheese mixture in three additions. Be careful not to deflate the batter.

**Prepare the Water Bath:**

Pour the batter into the prepared cake pan. Tap the pan gently to release any air bubbles. Place the pan in a larger baking tray and fill the tray with hot water until it reaches halfway up the sides of the cake pan.

**Bake:**

Bake for 25 minutes at 320°F (160°C), then reduce the temperature to 280°F (140°C) and bake for an additional 55 minutes.

**Cool Gradually:**

Turn off the oven and leave the cheesecake inside with the door slightly ajar for 15 minutes. Remove from the oven and let cool completely at room temperature before removing from the pan.