Step 1: Preheat your oven to 325°F (160°C). Prepare an 8-inch round springform pan by lining the bottom with parchment paper and greasing the sides. Wrap the outside of the pan tightly with two layers of heavy-duty aluminum foil to prevent water from seeping in during the water bath.
Step 2: In a heatproof bowl, combine the softened cream cheese, softened butter, and whole milk. Place the bowl over a saucepan of simmering water (creating a bain-marie or double boiler). Stir constantly until the mixture is smooth and completely melted. Remove the bowl from the heat.
Step 3: Add the egg yolks one at a time to the cream cheese mixture, whisking well after each addition until thoroughly combined. Stir in the lemon juice or vanilla extract.
Step 4: Sift the all-purpose flour and cornstarch directly into the cream cheese mixture. Whisk gently until just combined and the batter is smooth. Be careful not to overmix, which can develop gluten and toughen the cheesecake. Set aside.
Step 5: In a separate, very clean, large bowl, beat the egg whites with an electric mixer on medium speed until foamy. Gradually add the granulated sugar (reserving 1/4 cup for later) and increase the speed to high. Continue beating until you achieve soft to medium peaks. The meringue should be glossy and hold its shape when the whisk is lifted, but not be stiff and dry.
Step 6: Gently fold about one-third of the meringue into the cream cheese mixture using a spatula to lighten it. Then, carefully fold in the remaining meringue in two additions, using a cutting and folding motion to incorporate it fully while preserving as much air as possible. Do not deflate the meringue.
Step 7: Pour the fluffy batter into your prepared springform pan. Gently tap the pan on the counter a few times to release any large air bubbles. Place the springform pan into a larger roasting pan. Carefully pour hot water into the roasting pan until it reaches about halfway up the sides of the springform pan (this is the water bath).
Step 8: Carefully transfer the roasting pan to the preheated oven. Bake for 25-30 minutes at 325°F (160°C). After this time, reduce the oven temperature to 285°F (140°C) and continue baking for another 40-45 minutes, or until the top is golden brown and the cheesecake is set but still slightly jiggly in the very center when gently shaken.
Step 9: Turn off the oven, crack the door open slightly (you can prop it with a wooden spoon), and let the Fluffy Japanese Cheesecake cool inside the oven for at least 1 hour. This gradual cooling prevents the cheesecake from cracking or shrinking too much.
Step 10: Once completely cool, remove the cheesecake from the oven and the water bath. Loosen the sides of the pan with a thin knife if necessary, then carefully unmold. Refrigerate the cheesecake for at least 4 hours, or preferably overnight, before slicing and serving. Store any leftovers in an airtight container in the refrigerator.