Preheat the oven to 180°C (350°F).
In a bowl, combine the graham cracker crumbs, melted butter, and sugar.
Press the mixture into the bottom of a greased 9-inch springform pan.
Bake for 8-10 minutes until golden, then remove and let it cool.
In a large mixing bowl, beat the softened cream cheese with sugar until smooth.
Add the heavy cream, lemon juice, lemon zest, and vanilla extract. Beat until combined and creamy.
If you prefer a thicker texture, mix in the cornstarch.
Pour the cheesecake filling over the cooled crust in the springform pan.
Bake for 45-50 minutes, or until the center is set and slightly jiggles.
Let the cheesecake cool to room temperature, then refrigerate for at least 4 hours or overnight.
Before serving, garnish with additional lemon zest and lemon slices.