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 3 packages of the 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.
Blend in the eggs, one at a time, beating the batter well after each one.
Blend in heavy cream.
Gently spoon the cheese filling on top of the baked sponge cake layer.
Keep foil on outside of springform pan and place pan in a large shallow pan containing hot water that comes about 1 inch up the side of the pan. (Or use a moat pan)
Bake the cheesecake at 350 until the center barely jiggles when you shake the pan, about 60 minutes.
Cool in the oven 30 minutes with the oven shut off and the door cracked open.
Then cool on counter to room temp and refrigerate until it's completely cold, at least 4 hours or overnight.