Preheat and prepare the pan. Preheat your oven to 300°F (150°C) and line the bottom and sides of a 6-inch round baking pan with parchment paper.
Melt the butter and cream cheese over a double boiler. Fill a small saucepan halfway with water and bring it to a boil. Place a heatproof mixing bowl on top of the saucepan, ensuring it doesn’t touch the water. Add the cream cheese, butter, and milk to the bowl, whisking until the butter and cream cheese are fully melted and combined. Heat the mixture to approximately 130°F (55°C).
Add the egg yolks and vanilla. Remove the bowl from the heat and whisk in the egg yolks and vanilla extract until the mixture is smooth and fully combined.
Sift in the cake flour. Sift the cake flour and cornstarch into the mixture using a fine mesh sieve. Whisk until the batter is smooth and lump-free. To ensure a silky texture, pour the batter through the sieve once more to remove any remaining lumps.
Make the meringue. In a large mixing bowl, combine the egg whites and lemon juice. Using an electric hand mixer on high speed, beat the egg whites until white and frothy. Gradually add the sugar in three batches while continuing to mix. Beat until the meringue reaches medium soft peaks—when you lift the mixer, the peaks should slowly fold over, resembling soft-serve ice cream. Once soft peaks form, reduce the mixer speed to low and mix for an additional 30 seconds to eliminate any large bubbles.
Incorporate the meringue into the egg batter. Start by folding 1/3 of the meringue into the egg batter. Gently mix until fully combined and smooth. Next, pour the egg batter into the remaining meringue and carefully fold the mixture together with a rubber spatula. Fold just until combined, taking care not to over-mix and deflate the batter.
Prepare the pan. Pour the batter into the prepared baking pan, holding the bowl about 5 inches above the pan to help pop any remaining large air bubbles. Place the pan into a larger deep baking tray and fill the tray with 1-2 cm of hot boiling water.
Bake. Bake the cheesecake at 300°F (150°C) for 30 minutes. Lower the oven temperature to 230°F (110°C) and bake for another 30 minutes. Finally, increase the temperature to 275°F (135°C) and bake for an additional 13-15 minutes. Keep a close eye on the cake to prevent cracking. If cracks begin to form, it may indicate the oven is too hot. In that case, briefly open the oven door for about 5 seconds to release some steam. The cake is ready when the top is golden and a toothpick inserted into the center comes out mostly clean.
Cool. Once the cake is finished baking, turn off the oven and leave the cheesecake inside with the door slightly ajar for 15 minutes. Remove the water bath and let the cake sit in the oven for another 15 minutes to prevent drastic temperature changes, which can cause the cake to shrink. Take the cake out of the pan and place it on a cooling rack to cool completely. Dust the top with powdered sugar before serving and enjoy!