Preheat your oven to 325°F (165°C). Tightly wrap the outside of a 9-inch springform pan with a large sheet of heavy-duty aluminum foil. In a bowl, mix the vanilla wafer crumbs, sugar, and melted butter. Press this mixture firmly onto the bottom and about 1 inch up the sides of the pan. Place the pan in the freezer for at least 15 minutes.
To make the filling, use an electric mixer on medium speed to beat the softened cream cheese, sugar, and cornstarch until completely smooth, scraping the bowl as needed. Mix in the vanilla extract. Add the eggs one at a time, mixing on low speed just until each is blended.
Gently fold in the room-temperature sour cream with a spatula until just combined. Pour the filling into the chilled crust. Place the springform pan into a larger roasting pan. Carefully pour enough hot water into the roasting pan to come halfway up the sides of the springform pan.
Bake for 70 to 80 minutes. The cheesecake is done when the edges are set but the center still has a slight wobble. An instant-read thermometer inserted into the center should read 150°F (65°C). Turn off the oven, prop the door open slightly with a wooden spoon, and let the cheesecake cool in the oven for 1 hour.
Carefully remove the cheesecake from the water bath and place it on a wire rack. Run a thin knife around the edge of the cheesecake to loosen it from the pan. Let it cool completely to room temperature, which takes about 2 hours. Cover with plastic wrap and refrigerate for at least 8 hours, or overnight.
For the topping, whisk the brown sugar, corn syrup, cornstarch, egg yolks, and salt together in a medium saucepan. Gradually whisk in the half-and-half until smooth. Place the saucepan over medium heat.
Cook, whisking constantly, until the mixture thickens and begins to bubble, which should take about 5 to 7 minutes. Remove the pan from the heat. Stir in the butter and vanilla until the butter is fully melted, then fold in the toasted pecans.
Let the pecan topping cool for about 20 minutes, stirring it occasionally. Pour the warm topping over the top of the fully chilled cheesecake and spread it into an even layer. Return the cheesecake to the refrigerator for at least 1 more hour to allow the topping to set before slicing and serving.