1. Preheat the oven to 350°F. Generously butter the bottom and sides of a 9-inch springform pan. Wrap the outside with aluminum foil, covering the bottom and extending all the way up the sides. Make and bake the cake crust and leave it in the pan. Keep the oven on.
2. Put one package of the cream cheese, 1/3 cup of the sugar, and the cornstarch in a large bowl and beat with an electric mixer on low until creamy, about 3 minutes, scraping down the bowl several times. Blend in the remaining cream cheese, one package at a time, scraping down the bowl after each one.
3. Increase the mixer speed to medium and beat in the remaining 1 1/3 cups sugar, then the vanilla. Blend in the eggs, one at a time, beating well after adding each one. Beat in the cream just until completely blended. Be careful not to overmix! Gently spoon the batter over the crust.
4. Place the cake in a large shallow pan containing hot water that comes about 1 inch up the sides of the springform. Bake until the edges are light golden brown and the top is slightly golden tan, about 1¼ hours. Remove the cheesecake from the water bath, transfer to a wire rack, and let cool for 2 hours (just walk away-don’t move it). Then, leave the cake in the pan, cover loosely with plastic wrap, and refrigerate until completely cold, preferably overnight or for at least 4 hours.
5. To serve, release and remove the sides of the springform, leaving the cake on the bottom of the pan. Place on a cake plate. Refrigerate until ready to serve. Slice the cold cake with a sharp straight-edge knife, not a serrated one. Cover any leftover cake and refrigerate or wrap and freeze for up to 1 month.
To Make an 8-inch Cake:
Make an 8-inch sponge cake crust and use the cheesecake filling ingredient amounts as follows: three 8-ounce packages cream cheese, 1/3 cups sugar, 3 tablespoons cornstarch, 1 tablespoon pure vanilla extract, 2 extra-large eggs, and 2/3 cup heavy or whipping cream. The cooking time will be about the same.