Step 1: Preheat your oven to 325°F (160°C). Grease and line the bottom and sides of an 8-inch round springform pan with parchment paper, allowing it to extend a couple of inches above the rim. Wrap the outside of the pan with a double layer of aluminum foil to prepare for a water bath.
Step 2: In a heatproof bowl set over a saucepan of simmering water (bain-marie), combine the room temperature cream cheese, butter, and Greek yogurt. Stir constantly until the mixture is smooth and fully melted, resembling a thick, creamy sauce. Remove from heat.
Step 3: Whisk the egg yolks into the cream cheese mixture one at a time until thoroughly combined. Sift in the cornstarch and mix until no lumps remain. Add the lemon juice and vanilla extract, stirring until everything is well incorporated.
Step 4: In a separate, clean, dry bowl, beat the egg whites with an electric mixer on medium speed. Gradually add the granulated sugar, increasing the speed to high. Continue beating until stiff, glossy peaks form. The meringue should hold its shape when you lift the beaters.
Step 5: Gently fold one-third of the meringue into the cream cheese batter using a spatula. Be careful not to deflate the meringue. Once partially combined, fold in the remaining meringue in two additions until just combined. The mixture should be light and airy.
Step 6: Pour the batter into your prepared springform pan. Gently tap the pan on the counter a few times to release any large air bubbles.
Step 7: 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 water bath is crucial for even baking and preventing cracks.
Step 8: Bake for 15 minutes at 325°F (160°C). Then, reduce the oven temperature to 285°F (140°C) and bake for another 45-55 minutes, or until the cheesecake is golden brown on top and the center is just set but still slightly jiggly when gently shaken.
Step 9: Turn off the oven and prop the oven door open slightly. Let the cheesecake cool inside the oven for 1 hour. This slow cooling prevents cracking and helps maintain its delicate structure. Do not remove it abruptly!
Step 10: Remove the cheesecake from the oven and the water bath. Let it cool completely on a wire rack at room temperature. Once cool, cover it and refrigerate for at least 4 hours, or preferably overnight, before serving.