Preheat oven to 325°F (163°C). Lightly grease a 9-inch springform pan.
Mix graham cracker crumbs, sugar, and melted butter in a bowl. Press into the bottom of the pan. Bake for 10 minutes and let cool.
In a large bowl, beat cream cheese and sugar until smooth. Add eggs one at a time, then mix in vanilla and sour cream.
Pour filling into crust. Bake for 55-60 minutes until center is set. Turn off oven, crack door, and cool cheesecake for 1 hour.
Chill in the refrigerator for at least 4 hours or overnight.
For the caramel, heat sugar in a saucepan over medium heat, stirring constantly until melted and amber-colored.
Add butter and stir until melted. Slowly add cream (it will bubble), stir until smooth, then stir in sea salt.
Let caramel cool slightly, then pour over chilled cheesecake before serving.