For crust: Wrap foil tightly around outside of 9-inch-diameter springform pan. Blend hazelnuts and sugar in food processor until nuts are finely ground. Add melted butter; blend until moist clumps form. Press nut mixture onto bottom (not sides) of prepared pan.
For filling: Preheat oven to 350F. Beat cream cheese, sugar and vanilla in large bowl until well blended. Beat in eggs 1 at a time. Pour filling over crust. Bake until cheesecake puffs and is set around sides but center still moves slightly when pan is gently shaken, about 50 minutes. Transfer cheesecake to rack. Run small sharp knife around pan sides to loosen cake. Cool cake completely. Remove foil from pan. Cover with plastic and chill overnight.
For caramel sauce: Stir sugar and 1/4 cup water in heavy medium saucepan over medium heat until sugar dissolves. Increase heat; boil without stirring until syrup turns deep amber, occasionally brushing down sides of pan with wet pastry brush and swirling pan, about 7 minutes. Remove from heat; add cream (mixture will bubble vigorously). Boil sauce until reduced to 2 cups, stirring occasionally, about 5 minutes. Cool.
Spoon 1/2 cup caramel sauce evenly over top of cheesecake, leaving 1/2-inch border around edge. Arrange additional hazelnuts decoratively around outside edge of cake. Cover and refrigerate cheesecake until topping sets, about 2 hours. (Can be prepared 1 day ahead. Keep cheesecake refrigerated. Cover and refrigerate remaining sauce.)
Release pan sides from cheesecake. Transfer cake to platter. Rewarm remaining sauce just until pourable but not warm. Slice cheesecake. Serve, passing sauce separately.
Per serving: 10073 Calories (kcal); 815g Total Fat; (71% calories from fat); 151g Protein; 596g Carbohydrate; 2610mg Cholesterol; 3794mg Sodium Food Exchanges: 3 Grain(Starch); 19 Lean Meat; 0 Vegetable; 0 Fruit; 153 Fat; 33 1/2 Other Carbohydrates