In a large bowl, using an electric mixer fitted with the paddle attachment, beat 1 package of the cream cheese, 1/3 cup of the sugar, and the cornstarch together on low until creamy, about 3 minutes, scraping down the bowl several times.
Blend in the remaining cream cheese, one package at a time, beating well and scraping down the bowl after each.
Increase the mixer speed to medium and beat in the remaining sugar, then the vanilla.
Blend in the eggs, one at a time, beating well after each.
Beat in the cream just until completely blended.
The filling will look light, creamy, airy, and almost like billowy clouds. Be careful not to overmix! Gently spoon the batter over the crust. Wrap the sides of the pan in aluminum foil.
Place the cake pan in a large shallow pan containing hot water that comes halfway (about 1 inch) up the side of the springform. (Alternatively, use a cheesecake moat-my fave!) Bake until the edge is light golden brown, the top is light gold, and the center barely jiggles, about 1 1/4 hours. If the cake still feels soft around the edge, let it bake for 10 minutes more (the cooking time will be about the same for both the 8- and 9-inch cheesecakes). Remove the cheesecake from the water bath, transfer to a wire rack, and let cool for 2 hours. Chill until cold for hours.
