How to Make It
Preheat the oven to 425°. In a medium saucepan, combine the sugar and water. Boil over moderately high heat, without stirring, washing down any crystals that form on the side of the pan, until a deep amber caramel forms, 6 to 8 minutes. Remove from the heat and stir in the cream; the sauce will bubble up. Pour the caramel into a heatproof cup and let cool slightly. Stir in the balsamic vinegar; keep warm.
Heat a rimmed baking sheet in the oven. In a bowl, toss the pears with the melted butter and salt. Spread the pears on the hot baking sheet and roast, stirring once, until golden around the edges and tender, 15 minutes; transfer to a plate to cool.
Reduce the oven temperature to 350°. Spread the hazelnuts in a pie plate and toast for 7 minutes; transfer to a cutting board and coarsely chop.
Spoon the pears into bowls and top with vanilla ice cream. Pour the balsamic-caramel sauce on top, sprinkle with the hazelnuts and serve.