For crust: Wrap foil tightly around outside of a 9-inch round springform pan.
In food processor, blend hazelnuts and sugar together until ground finely.
Mix in the melted butter until it forms moist clumps.
Press onto the bottom of the pan only. Do not coat the sides.
For filling: Preheat oven to 350 F (325 F for dark pans).
Using an electric mixer, beat the cream cheese, sugar and vanilla together in a large bowl until well mixed.
Add the eggs one at a time, and beat just until well blended.
Pour filling into the pan.
Bake until cheesecake is puffy and the edges are set. The center should still wobble ever so slightly when gently shaking the pan, about 50 minutes.
Set pan onto a wire rack, and run a sharp knife around the edges.
Cool cake completely.
Remove the foil. Cover the cake with plastic wrap and refrigerate overnight.
For caramel sauce: Mix sugar and water in a heavy-duty medium saucepan. Heat over medium heat until the sugar is completely dissolved.
Raise the heat to high, and boil without stirring until the syrup becomes a deep amber color. While heating, brush down the sides of the pan occasionally with a wet pastry brush. Also, occasionally swirl the pan. The whole process should take about 7 minutes.
Remove from the heat and carefully add the cream (the mixture will bubble).
Keep boiling until the sauce is reduced to 2 cups, stirring occasionally, about 5 minutes. Cool completely.
Evenly distribute 1/2 cup of the caramel sauce on top of the cheesecake, leaving a 1/2-inch border from the edges.
Place hazelnuts around the outside edges.
Cover and chill until the topping is fully set, about 2 hours.
(Can be prepared 1 day ahead, if you keep cheesecake covered and chilled. Refrigerate any remaining sauce.).
To serve: Remove sides of pan, and transfer cake to serving plate.
Rewarm remaining sauce just until pourable but not warm.
Cut cheesecake into slices. Pass around the sauce separately.