Preheat oven to 350°F. Grease a 9-inch springform pan.
Olive Oil & Sea Salt Base: In a medium bowl, mix together graham cracker crumbs, white sugar, olive oil, and sea salt. Pour mixture into the prepared pan. Using the bottom of a flat glass, press the mixture down to form an even layer. Bake for 10 minutes.
Plain Filling: In a large bowl, beat Norman's Kosher Cholov Yisroel Cream Cheese, white sugar, and vanilla extract until smooth. Add eggs, one at a time, beating well after each addition. Pour mixture over the prepared crust.
Bake for 50-60 minutes, or until the edges are lightly golden and the center is almost set. Let cool in the pan for 10 minutes, then run a knife around the edge of the cake to loosen it. Let cool completely, then chill in the refrigerator for at least 2 hours before serving.
Caramel Sauce Topping: In a medium saucepan, combine white sugar and water. Cook over medium-high heat, stirring constantly, until the sugar dissolves and the mixture turns amber in color. Remove from heat, then stir in heavy cream, unsalted butter, and sea salt until smooth. Let cool slightly.
Pour caramel sauce over the chilled cheesecake. Use a knife or spatula to spread the sauce evenly over the top. Serve chilled.