For the crust:
Heat the oven to 325ºF and arrange the 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 prepared springform pan; set aside.
For the cheesecake:
Combine cream cheese and sugar in a stand mixer fitted with a paddle and mix over medium speed until light, airy, and smooth. Add the eggs one at a time, mixing completely after each addition. Add the vanilla extract and mix until blended.
Pour 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 door slightly ajar, and let cheesecake cool completely.
For the caramel:
Stir together sugar and 1 tablespoon water in a small saucepan. Place over medium-high heat and bring to a boil. Let boil until amber in color, about 3 minutes. Immediately add butter and stir to incorporate. Remove from heat, add cream, and mix well. Set aside and let cool to room temperature.
Pour the caramel over the cooled cheesecake, then scatter the pecan pieces and sea salt over the top.
Cook time includes about an hour for the cheesecake to cool while in the oven, once the oven is turned off, this time may vary.
Remember, cooking times may vary depending on ovens, so test doneness before stated cooking times.