For caramel sauce, bring sugar, water and vinegar up to a full rolling boil. Boil sugar, uncovered and without stirring until a rich amber colour, brushing down the sides of the pot with cool water often. Remove from heat and whisk in cream (watch out for steam). Set aside to cool, then chill until ready to use.
For cake, grease and line the bottom and sides of a 9-x-13-inch pan with parchment paper. Preheat oven to 350 F (180 C).
Combine cookie crumbs with ½ cup of toffee bits and melted butter. Press into bottom of prepared pan and bake for 12 minutes. Place hazelnuts on a baking tray and toast for 10 minutes, stirring once.
Soften dulce de leche ice cream on counter for 15 minutes, then beat slightly to soften. Spread into cooled pan and freeze for 30 minutes.
Spread half of caramel over ice cream and sprinkle with ½ cup toasted hazelnuts and remaining ½ cup of toffee bits. Freeze while preparing white chocolate layer.
Soften white chocolate ice cream on counter for 15 minutes, then beat slightly to soften. Spread over hazelnut-toffee layer and freeze for 30 minutes. Drizzle top cake with remaining caramel sauce and freeze for 4 hours.
To serve, remove cake from pan and press remaining 1 cup of toasted hazelnuts on side of cake. Let cake sit out for 10 or 15 minutes before slicing.