Place the chestnuts, milk, sugar, fennel seeds, and salt in a medium saucepan over medium heat and bring to a simmer. Reduce heat to low and continue to simmer, stirring often to break up the chestnuts. Continue to simmer and stir until all of the milk has been absorbed.
While the chestnuts are simmering, melt the chocolate using a double boiler. Set aside.
When chestnuts are cooked, rice into a large mixing bowl, small amounts at a time. Add cognac and melted chocolate and fold together using a rubber spatula until smooth. (Make sure there are no pockets of unmixed chestnuts). The mixture should resemble cookie dough. Pack the dough into a smaller bowl, cover with plastic, and refrigerate for at least one hour (or overnight).
When you're ready to serve, whip cream with powdered sugar and vanilla until the mixture forms soft peaks.
Traditionally, Italians rice the dough a second time onto a large platter to form a mountain. Spoon whipped cream atop the mountain and finish with a cherry. This tradition is an homage to Monte Bianco, the highest mountain in the Alps.
At Babbo, we freeze or chill the dough into a log, then serve is sliced with candied chestnuts. Alternatively, simply rice your dough into small bowls and pipe or spoon a dollop of cream on top. Then dig in!