Preheat the oven to 350 F and generously butter a 9-inch springform pan.
In a mixing bowl, combine crumbs, sugar and butter. Press into bottom of pan.
Set pan on a large sheet of heavy duty foil. Bring foil and up and around the side of the pan and press it tightly into the sides to make bottom water-proof. Do this (at least) twice. Bake crust on center rack for 8-10 minutes. Let cool.
Place one 8-ounce package 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 minute, then beat in the remaining 3 packages of softened cream cheese.
Increase the mixer speed to high and beat in the sugar, then beat in the vanilla, lemon extract ( if using) and heavy cream. Blend in the eggs, one at a time, stirring only until completely blended. Over-beating the eggs contributes to cracking, so don’t beat too much air into the batter at this point.
Spoon the cheese filling on top of the crumb layer. Set the foil-wrapped pan in a large shallow pan and add hot water so that water comes about 1 inch up the sides of the springform pan. Bake the cheesecake until the center barely jiggles when you shake the pan – 55 minutes to an hour.
Cool the cake on a wire rack for 1-2 hours, then refrigerate until it's completely cold -- at least 4 hours or overnight.
Remove the sides of the springform pan and serve from pan bottom or transfer to a platter. Serve with fruit topping if desired.