Step 1: Preheat your oven to 325°F (160°C). Line a 12-cup muffin tin with paper liners. Place the muffin tin inside a larger baking pan for the water bath. Boil some water for the water bath and set aside.
Step 2: In a heatproof bowl, combine the softened cream cheese, milk, and butter. Place the bowl over a pot of simmering water (creating a double boiler), making sure the bowl does not touch the water. Whisk until the mixture is smooth and melted. Remove from heat.
Step 3: Stir in the egg yolks, lemon juice (if using), and vanilla extract into the cream cheese mixture until well combined. Sift the all-purpose flour and cornstarch into the mixture and whisk gently until just incorporated and smooth. Set aside.
Step 4: In a separate, very clean bowl, whip the egg whites with an electric mixer until foamy. Gradually add half of the granulated sugar (1/4 cup) and continue whipping until soft peaks form. Add the remaining half of the sugar and whip until you achieve soft to medium-stiff, glossy peaks. The meringue should hold its shape but still be slightly pliable.
Step 5: Gently fold one-third of the meringue into the cream cheese batter to lighten it. Then, carefully fold in the remaining meringue in two additions, using a spatula to gently incorporate without deflating the mixture. Be careful not to overmix.
Step 6: Divide the batter evenly among the 12 prepared muffin cups, filling each about two-thirds full. Carefully pour the hot water into the larger baking pan around the muffin tin, ensuring it comes up about 1 inch (2.5 cm) high.
Step 7: Bake for 30-35 minutes, or until the tops are golden brown and the cheesecakes are set but still slightly jiggly in the center. The baking time may vary based on your oven.
Step 8: Once baked, turn off the oven, crack the oven door open slightly, and let the cupcakes cool inside for 15-20 minutes. This gradual cooling prevents cracking and deflation. Remove from the oven and water bath, then cool completely on a wire rack before refrigerating for at least 4 hours, or preferably overnight, to set the texture and flavors.