Start by preheating your oven to 350°F, with the rack in the middle-lower part. Grease a 9-inch springform pan generously with butter, then wrap the bottom and sides tightly with foil so no water can sneak in later. Set it aside.
Crush your graham crackers in a food processor until you have fine, sandy crumbs. Mix in the melted butter until it looks like damp sand that clumps easily between your fingers. Pour this mixture into your pan and press it firmly and evenly across the bottom. Bake for 8 to 10 minutes, until it starts to turn lightly golden. Take it out and let it cool completely while you prepare the filling.
Now, in a large mixing bowl, beat together the cream cheese, sour cream, sugar, cornstarch, salt, lemon juice, and vanilla extract on medium speed for about 5 minutes, until the mixture is silky smooth with no lumps. Use a spatula to scrape the sides and bottom often — Grandma always says that’s where the little pockets of cream cheese like to hide.
Add the eggs, one at a time, mixing on low just until they’re blended. Don’t overbeat — you want the batter to stay soft and creamy. Pour the mixture over your cooled crust.
Set your wrapped springform pan into a larger baking dish and pour in boiling water until it reaches about 2 inches up the sides. This gentle water bath keeps the cheesecake smooth and prevents cracking. Bake at 350°F for 55 minutes, until the edges are puffed but the center still has a gentle jiggle.
When it’s done, turn off the oven and leave the cheesecake inside with the door slightly open for about an hour to cool slowly. Then transfer the pan to a wire rack and let it cool completely before placing it in the refrigerator. Chill it overnight, uncovered, to let it set beautifully.
Before serving, take the cheesecake out and let it sit at room temperature for about 30 minutes. Carefully unmold it, place it on your serving plate, and get ready for the finishing touch.