Spread the peanuts on a sheet pan and roast for 7 minutes, until they become fragrant. Pour into a medium bowl, add the popcorn, and set aside. Line the sheet pan with parchment paper.
Place the sugar and 1/4 cup water in a medium (10-inch) saute pan and mix with a fork until all the sugar is moistened. Cook over medium-high heat until the sugar dissolves--from this point on, don't stir the caramel, swirl the pan! (Don't worry if the mixture looks as though it's crystallizing.)
Continue to cook for 5 to 10 minutes until it becomes a clear golden brown, swirling the pan constantly at the end. (Be careful, the caramel is very hot!) Off the heat, quickly add the corn syrup and vanilla (it will bubble up!) and swirl the pan to combine. Working quickly (the caramel will continue to cook in the pan), add the popcorn and nut mixture plus the kosher salt and toss with two large spoons until the popcorn and nuts are completely coated.
Pour the mixture plus any extra caramel in the pan onto the prepared sheet pan and spread the mixture out in one layer, pulling it apart with two forks. Sprinkle with the fleur de sel and set aside to cool. When it's completely cooled, carefully break into large clusters with your hands.
To serve, pour puddles of Chocolate Sauce into shallow bowls. For each serving, place 3 small scoops of gelato on the chocolate sauce, sprinkle with some of the caramelized popcorn, and add a dollop of the Sweetened Whipped Cream in the middle. Serve immediately.
Place the chocolate, cream, corn syrup, and coffee in a bowl set over a pan of simmering water. Be sure the water doesn't touch the bottom of the bowl. Heat the mixture, stirring occasionally, until the chocolate melts and the mixture is smooth. Serve warm.
Sweetened Whipped Cream:
Pour the cream into the bowl of an electric mixer fitted with the whisk attachment. Add the sugar and vanilla and beat on high speed until the cream forms soft peaks.