MAKE THE CRUST: Preheat the oven to 375 degrees. Line a baking sheet with parchment paper. Wrap the outside of a 10-inch round springform pan with foil.

In a medium bowl, toss the pecans with 1/2 teaspoon of the butter, 1/2 tablespoon of the granulated sugar, the brown sugar, the cream, and salt. Spread the nuts on the prepared baking sheet and arrange them, right side up in a single layer. Bake for about 18 minutes, until the sugar is caramelized and the pecans are toasted. Let cool.

Transfer all but 12 of the pecans to a food processor. Add the graham crackers and pulse until finely ground. Add the remaining stick of melted butter and 1/3 cup of granulated sugar and pulse until the crumbs are moistened. Press the crumbs over the bottom of the pan and two-thirds of the way up the side of the prepared springform pan.

MAKE THE FILLING: In a clean food processor, pulse the cream cheese with the sugar until smooth. Add the eggs, one at a time, and pulse until incorporated. Scrape down the side of the bowl. Pulse in the vanilla and sour cream. Scrape the batter into the pan and bake in the center of the oven for about 1 hour, until the top of the cheesecake is lightly golden in spots and the center is slightly jiggly. Transfer the cake to a rack and let cool completely. Wrap in plastic and refrigerate overnight.

Unwrap the cheesecake and discard the foil. Remove the ring and transfer the cake to a plate. Arrange the 12 reserved pecans on top. Using a warm, slightly moistened knife, cut the cake into wedges, wiping and rewetting the blade between slices. Transfer the slices to plates and pour some of the Caramel Sauce on top. Serve with the remaining Caramel Sauce.

The cheesecake can be refrigerated for up to 5 days.