Mix the cornstarch and water in a small bowl until smooth. Set aside.
Using an electric hand mixer or a stand mixer, beat the cream cheese on low speed for 2 to 3 minutes, until smooth and free of any lumps. Next, add the sugar and sour cream and continue mixing until creamy and well incorporated. Gradually add the sweetened condensed milk, scraping down the bowl as necessary, and continue beating for 2 minutes. Next, add the heavy cream, lemon juice, lemon zest, vanilla extract, and cornstarch mixture; beat on high speed until well incorporated, about 1 minute.
Pour the batter over the baked crust and spread it into an even layer. Spoon small dollops of blueberries sauce over the cheesecake filling (add as much or as little as you like), then use a toothpick or knife tip to swirl everything together gently.
Bake for 30 to 35 minutes, or until the edges are set and slightly puffy, and the centers only slightly jiggle.
Remove from oven. Set the pan on a wire rack and allow it to cool at room temperature for 2 hours, then transfer to the refrigerator and chill for at least 3 hours or up to 24 hours.
To slice, use the parchment overhang to lift the bars out of the pan as a whole, then cut into squares with a sharp knife. For extra-neat squares, wipe the knife clean between each cut. Refrigerate until ready to serve.