Prepare the crust: Preheat your oven to 325°F (163°C). In a medium bowl, mix the graham cracker crumbs, sugar, and melted butter. Press the mixture into the bottom of a 9-inch springform pan, ensuring an even layer. Bake for 10 minutes, then remove from the oven and let cool.
Make the cheesecake filling: In a large bowl, beat the softened cream cheese until smooth. Add the sugar and mix until creamy. One at a time, add the eggs, mixing well after each addition. Stir in the vanilla extract and sour cream until fully combined. Fold in the chopped pecans.
Bake the cheesecake: Pour the cheesecake filling over the cooled crust, spreading it evenly. Place the springform pan on a baking sheet and bake for 55-60 minutes, or until the center is set but still slightly jiggly. Turn off the oven and let the cheesecake cool in the oven with the door slightly open for 1 hour.
Make the caramel sauce: In a medium saucepan over medium heat, melt the sugar, stirring constantly, until it turns a deep amber color. Carefully add the butter and whisk until melted. Slowly pour in the heavy cream, stirring constantly. Let the caramel boil for 1-2 minutes, then remove from heat and stir in the sea salt.
Assemble: Once the cheesecake has cooled completely, pour the caramel sauce over the top. Garnish with pecan halves around the edges. Chill the cheesecake in the refrigerator for at least 4 hours or overnight before serving.
