Using a rolling pin or in a food processor, crush graham crackers into crumbs. Then add in the sugar and melted butter. Mix well.
Lightly grease a 7-inch springform pan, then line the bottom with parchment paper.
Pour the crumb mixture into the prepared pan. Pack it in tightly on the entire bottom of the pan and slightly up sides of the pan. Set aside.
In a large mixing bowl with an electric mixer or in a bowl of a stand mixer, mix cream cheese with sugar and corn starch. Mix until fully blended.
Add the sour cream, lime zest, lime juice, and vanilla and beat until smooth.
Next, add the eggs and the egg yolk. Beat as little as possible just until they are fully combined.
Pour the cheesecake mixture over the prepared crust. Lightly tap the pan on the counter several times to release any air bubbles.
Preheat the oven to 375F.
Bake cheesecake in a water bath at 375F for 1 hour. The edges should be firm and the center of the cheesecake should still be slightly jiggly.
Turn off the oven and crack the oven door. Let the cheesecake cool in the oven for about an hour.
Then remove from oven and cover and refrigerate overnight.
You can serve as is or before serving the cheesecake, decorate it with whipped cream, berries, and key lime slices.