Make the sponge cake as the recipe directs.

Make the cream cheese filling:

Place one (8-ounce) package of the cream cheese, 1/3 cup of the sugar, and the cornstarch in a large bowl. Beat with an electric mixer on low until creamy, about 3 minutes. Then beat in the remaining three packages of cream cheese.

Increase the mixer speed to high and beat in the remaining 1 1/3 cups of the sugar. Then beat in the vanilla. Add the eggs, one at a time, beating the batter well after each one. Blend in the heavy cream. Mix the filling only until completely blended. Be careful not to overmix the batter.

Gently spoon the cheese filling on top of the baked sponge cake layer.

Place the springform pan in a large shallow pan containing hot water that comes about 1 inch up the sides of the pan. Bake the cheesecake until the center barely jiggles when you shake the pan, about 1 hour.

Cool the cake on a wire rack for 1 hour. Then, leaving the cake in the pan, cover it with plastic wrap and refrigerate until it’s completely cold, at least 4 hours or overnight.

Remove the sides of the springform pan. Slide the cake off the bottom of the pan onto a serving plate. (Or, if you wish, simply leave the cake on the removable bottom of the pan and place it on a serving plate.) If any cake is left over, cover it with plastic wrap and store for up to a week in the refrigerator.