Preheat the oven to 320 degrees. Grease the bottom and sides of a 9-by-3-inch round cake pan with 1 tablespoon of butter. Line the bottom of the pan with a round of parchment paper, and then line the sides. The butter will help the parchment paper stick.
In a small saucepan over medium heat, combine the remaining butter, the cream cheese, and the milk. Whisk until the butter and cream cheese are melted and smooth. Remove the saucepan from the heat and set it aside to cool.
Separate the egg whites from the egg yolks. Allow the egg whites to drip through your fingers into the bowl of a stand mixer fitted with a whisk attachment. Gently place the egg yolks into a separate large bowl.
Whisk the egg yolks until they are creamy, and then slowly add the cooled cream mixture to the yolks, whisking until well blended.
Pour the flour and cornstarch through a fine-mesh sieve over the large bowl with the creamy yolk mixture. Whisk until combined.
Add the cream of tartar to the egg whites in the bowl of the stand mixer. Beat the egg whites on high speed until they are frothy. Gradually add the sugar to the egg whites, continuing to beat until the whites are glossy and the peaks are stiff.
Using a silicone spatula, gently fold about 1/4 of the egg white mixture into the egg yolk mixture. Continue to fold more of the egg white mixture into the yolk mixture until the mixtures are thoroughly blended together.
Carefully pour the batter into the prepared cake pan. Gently tap the pan on the counter a few times to release any trapped air bubbles from the batter.
Place the cake pan with the cheesecake batter into the baking tray. Using a kettle or measuring cup, carefully fill the tray with 1 inch of hot water. Then put the tray in the oven.
Bake for 25 minutes. Then reduce the heat to 250 degrees and bake for another 55 minutes or until the cake has doubled in size and is golden brown on top.
Do not remove the cake from the oven. Turn the oven off and leave the oven door ajar for about 30 minutes. Sudden changes in temperature may cause the cake to deflate.
Remove the cheesecake from the oven and allow it to cool completely on the counter.
Invert the cake onto a plate and peel off the parchment paper. Garnish with powdered sugar. Enjoy!
A springform pan can be used in place of the 9-by-3-inch cake pan, but it may not yield the best results. Wrap the springform pan in 3 layers of aluminum foil to avoid water seeping in from the water bath. Line the springform pan with parchment paper the same way you would line the cake pan.
You can store this Japanese cheesecake in an airtight container in the refrigerator for 3 days.