Heat the oven to 350°F. Grease a 9-inch springform pan and wrap the outside bottom with foil if using a water bath.

Combine the graham-cracker crumbs, sugar, and melted butter. Press the mixture firmly over the bottom of the pan and bake for 8–10 minutes, then cool slightly.

Reduce the oven temperature to 325°F. Beat the softened cream cheese and sugar on medium-low speed until smooth, then mix in the cornstarch, sour cream, and vanilla.

Add the eggs one at a time, mixing only until each is incorporated. Pour the filling over the crust.

Bake for approximately 55–70 minutes, preferably in a shallow water bath, until the edges are set and the center still has a slight wobble.

Turn off the oven, crack the door, and let the cheesecake cool inside for about 30 minutes. Cool completely at room temperature, then refrigerate for at least 6 hours or overnight.

For the topping, melt the butter in a saucepan. Add the brown sugar, cream, corn syrup, and salt, then simmer gently for 2–4 minutes while stirring until smooth.

Remove the saucepan from the heat and stir in the vanilla and pecans. Cool the topping until warm rather than hot, then spread it over the chilled cheesecake and refrigerate briefly again before slicing.