Preheat the oven to 160°C (320°F). In a large mixing bowl, combine cream cheese and plain yogurt. Using an electric hand mixer or a stand mixer fitted with a paddle attachment, beat until the mixture is smooth and creamy with no lumps.
Add sugar and vanilla extract continue mixing until fully incorporated. Pour whipping cream and cornstarch, then mix again until the batter is completely smooth.
Pour half of the cheesecake batter into the prepared crust and spread evenly. Combine the remaining cheesecake batter with prepared strawberry pureed mixture, reserve a few spoons for a marbled topping(optional). Mix until it is smooth.
Gently pour the strawberry layer over the plain layer and swirl in a bit of strawberry topping for a marbled effect.
Place the pan in a water bath (or place a tray with boiling water on bottom rack to create steam). Bake for 50 to 55 minutes, or until the edges are set and slightly puffed, while the center remains slightly jiggly.
Turn off the oven, crack the door open slightly, and let the cheesecake cool inside for 45 minutes. Then remove it from the oven and Refrigerate the cheesecake for 4 to 5 hours, or until fully set and chilled through.