Heat oven to 325F. Stir graham cracker crumbs, melted butter, and sugar until the texture of wet sand. Press firmly into the bottom of a 9-inch springform pan, going about 1 inch up the sides. Bake 10 minutes until set and fragrant. Cool while you make the filling. Reduce oven to 300F.

Beat cream cheese on medium speed until completely smooth, 2 to 3 minutes, scraping the bowl twice. Add sugar and beat another 2 minutes until no graininess remains. The mixture should look silky, not fluffy.

Mix in sour cream and vanilla on low speed until just combined. Add eggs one at a time, beating on low just until each disappears into the batter. Do not overbeat. Pour into cooled crust and smooth the top.

Place the springform pan in a large roasting pan. Pour hot water into the roasting pan until it reaches halfway up the sides of the springform pan. Bake at 300F for 55 to 65 minutes, until the edges are set but the center still jiggles slightly when you tap the pan. Turn off the oven, crack the door open with a wooden spoon, and let the cheesecake cool inside for 1 hour.

Remove from the water bath, run a thin knife around the edge to loosen, and cool to room temperature. Cover and refrigerate at least 6 hours or overnight. The cheesecake must be completely cold before adding the topping.

Combine corn syrup, brown sugar, butter, and heavy cream in a medium saucepan over medium heat. Bring to a gentle boil and cook for 3 to 4 minutes, stirring constantly, until the mixture thickens slightly and reaches 220F on a candy thermometer. Remove from heat and stir in vanilla and toasted pecans. Let cool 10 minutes until thick but still pourable.

Remove the cheesecake from the springform pan and place on a serving plate. Spoon the warm pecan topping over the cheesecake, spreading to the edges and letting some drip down the sides. Chill 30 minutes to set the topping, or serve immediately if you prefer it warm and saucy.