For the crust:
1Heat the oven to 325ºF and arrange a rack in the middle. Butter the bottom and sides of a 9-inch springform pan; set aside. Mix together the graham cracker crumbs, butter, and sugar in a medium bowl until thoroughly combined. Evenly press the mixture into the bottom of the prepared springform pan; set aside.
For the cheesecake:
1Combine the cream cheese and sugar in a stand mixer fitted with a paddle attachment and mix on medium speed until light, airy, and smooth. Add the yolk and then the eggs one at a time, mixing completely after each addition. Add the vanilla extract and mix until blended.
2Pour the mixture into the prepared pan and bake until a toothpick or cake tester inserted into the cake comes out clean and the center of the cheesecake is just set, about 40 minutes. Turn off the oven, leave the door slightly ajar, and let the cheesecake cool completely.
For the caramel:
1Stir together the sugar and water in a small saucepan. Place over medium-high heat and bring to a boil. Let boil until the mixture turns amber in color, about 3 minutes. Immediately add the butter and stir to incorporate. Remove from heat, add the cream, and mix well. Set aside and let cool to room temperature.
1Pour the caramel over the cooled cheesecake, then scatter the pecan pieces and sea salt over the top.
Beverage pairing: Blandy’s 5 Year Old Bual Madeira, Portugal. Bual is a fairly full-bodied style of Madeira, dark and deeply flavored of nuts, chocolate, and molasses, which pairs well with this dessert. The wine’s surprising acidity, though, will make for a nice counter to the cheesecake’s richness. Serve slightly chilled.