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Special equipment: a 9-inch springform pan
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For the crust: Position a rack in the center of the oven, and preheat to 325 degrees F. Butter the inside of the springform pan.
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Pulse the graham crackers in a food processor until finely ground.
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Add the butter, sugar and salt, and pulse until the mixture comes together and holds its shape when squeezed.
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Pour the mixture into the prepared pan, and press it into the bottom to make an even layer.
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Bake until the crust is just firm, about 10 minutes.
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Remove and let cool completely.
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Place the pan on a large piece of foil, and fold the foil up the sides of the pan.
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(This helps seal the pan, to keep water out while baking.)
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For the filling: Wipe out the food processor.
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Pulse the cream cheese, sugar and sour cream until completely smooth, without any lumps, scraping down the sides of the bowl a few times.
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Add the eggs and vanilla, and pulse until incorporated.
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Pour the filling into the crust, and set the pan inside a roasting pan.
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Fill the roasting pan with enough hot water to go halfway up the sides of the springform pan (but not above the foil).
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Bake the cheesecake until the edge is set but the center jiggles slightly (when you gently shake the pan, the cheesecake should move in a cohesive wave motion), 1 hour 10 minutes to 1 hour 20 minutes.
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Turn the oven off, and open the door for a few seconds to let out some heat.
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Close the door, and let the cheesecake sit in the oven until cooked completely through, 1 hour more.
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Transfer the springform pan to a cooling rack.
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Run a knife around the edge, and let the cheesecake cool to room temperature.
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Wrap and refrigerate overnight or up to 2 days.
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For the topping: Preheat the oven to 350 degrees F. Spread the pecans out on a baking sheet, and bake until they turn a few shades darker and are nicely toasted, about 15 minutes.
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Let cool, then halve each pecan lengthwise.
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Meanwhile, heat the cream, butter, corn syrup, vanilla and salt in a small saucepan over medium heat until just steaming.
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Reduce the heat to low to keep the cream mixture warm.
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Cook the sugar in an even layer in a medium skillet over medium heat, without stirring, until it begins to melt.
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Gently swirl the pan as needed as the sugar continues to melt and begins to caramelize and turn lightly golden in spots.
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Keep cooking and swirling until the caramel is a uniform deep amber.
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Remove from the heat, and slowly whisk in the warm cream mixture (watch out for ferocious bubbles).
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Return the caramel sauce to medium heat, and cook to reduce slightly, about 2 minutes.
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Let cool.
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To see if the sauce is ready for topping the cheesecake, dip a spoon into it and let the sauce drop off; it's ready if it easily and slowly drips off the spoon.
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(The sauce can be refrigerated up to 2 days; reheat in the microwave.)
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To assemble: Spoon the sauce into the center of the cheesecake, and let it ooze to the edge.
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If needed, swirl the sauce with the back of a spoon to help it along.
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Sprinkle the pecans in a generous layer over the sauce.
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The cheesecake can now be served or refrigerated for up to 4 hours.
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To slice the cake, dip a sharp, heavy knife into warm water, wipe the knife dry and slice into the cake.
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Wipe the knife clean and repeat.
