Preheat oven to 350°F/180°C. Wrap the outside of a 9-inch springform pan (bottom and sides) with a large piece of foil.
In a medium bowl, mix together crumbs, sugar, and melted butter and mix until combined and moistened. Press mixture into the bottom of prepared pan to form an even layer of crumbs. Bake for 8-9 minutes until golden brown. Allow to cool completely on a wire rack. Meanwhile, prepare the filling.
Increase oven temperature to 425°F/220°C.
In a mixer fitted with the paddle attachment, beat cream cheese on medium-low speed until smooth and lump-free, 1-2 minutes. Add sugar and beat until blended. Scrape down the sides and bottom of the bowl as necessary. Add cornstarch and mix until blended. Add the eggs and beat until fully combined. Add cream, vanilla extract, and lemon zest and beat just until combined and smooth. Pour batter over cooled crust and spread evenly.
Bake cake for 10 minutes, then lower temperature to 225°F/110°C and continue to bake for 60 minutes until golden brown around the edges, the sides are set but the center is still slightly wobbly (some comments suggested this was not enough baking time. I baked this so many times and it works. If you're not sure if your oven temperature is accurate or if your baking time is usually longer than those called for in a recipe, you can add an additional 10-20 minutes, and avoid opening the oven door too many times). Turn off oven, open the oven door slightly or halfway to let in cold air, and leave the cake in the oven for 60 minutes. This will help prevent the cake from cracking and the cake will remain creamy. Transfer the cake to a wire rack and allow it to cool to room temperature. Cover the cake with plastic wrap and refrigerate overnight or for at least 12 hours.