Prepare the oven and pan: Preheat the oven to 300°F (150°C). Line the bottom and sides of a 6-inch round baking pan with parchment paper.
Melt the cream cheese mixture: Fill a small saucepan halfway with water and bring it to a boil. Place a heatproof mixing bowl over the saucepan, making sure it fits securely, then add the cream cheese, butter, and milk. Whisk until the butter and cream cheese have completely melted and the mixture reaches about 130°F (55°C). Add the yolks and vanilla: Remove the bowl from the heat. Whisk in the room-temperature egg yolks and vanilla extract until the mixture is evenly combined and smooth.
Sift the dry ingredients: Pass the cake flour and cornstarch through a fine-mesh sieve into the cream cheese mixture. Whisk until smooth, then strain the batter through the sieve once more to remove any remaining lumps.
Whip the meringue: Place the egg whites and lemon juice in a large mixing bowl. Using an electric hand mixer on high speed, beat until the whites are white and frothy. With the mixer running, gradually add the sugar in three batches, continuing to beat between additions. Stop when the meringue reaches medium-soft peaks that gently fold over when the beaters are lifted. Reduce the mixer to low and beat for another 30 seconds to remove larger air bubbles. Lighten the batter: Add one-third of the meringue to the egg-and-cream-cheese batter. Fold gently until completely incorporated and smooth.
Fold in the remaining meringue: Pour the lightened egg batter gently into the remaining meringue. Using a rubber spatula, fold carefully until just combined, taking care not to over-mix or deflate the air in the meringue.
Fill the pan: Pour the batter into the prepared 6-inch pan from about 5 inches above the pan. This helps release remaining large air bubbles.
Set up the water bath: Place the filled cake pan inside a larger, deep baking tray. Carefully add about 1–2 cm of hot boiling water to the larger tray, creating a water bath.
Bake the cheesecake: Bake at 300°F (150°C) for 30 minutes. Reduce the oven temperature to 230°F (110°C) and continue baking for another 30 minutes. Increase the temperature to 275°F (135°C) and bake for a final 13–15 minutes. Watch the cheesecake closely during baking. If it begins to crack, briefly crack the oven door for about 5 seconds to release steam. The cheesecake is ready when the top is golden and a toothpick inserted into the center comes out mostly clean. Cool gradually in the oven: Turn off the oven and leave the cheesecake inside with the oven door cracked for about 15 minutes. Remove the cake pan from the water bath, then return the cheesecake to the oven and leave it there for another 15 minutes. This gradual cooling helps prevent dramatic shrinking from a sudden temperature change. Cool completely: Remove the cheesecake from the pan and place it on a wire rack. Allow it to cool completely, then sift powdered sugar over the top before serving.
