To make the mousse: Place chocolate and milk in a medium heatproof bowl. Melt in the microwave or a double boiler until completely smooth. Stir in vanilla and hazelnuts. If mixture is warm, leave on the counter until it reaches room temperature.
In a mixer bowl, beat heavy cream until soft but stable peaks form. Gently fold half of the whipped cream into the cooled chocolate mixture until combined, then fold in the remaining whipped cream until combined and smooth. Divide into serving cups.
To make the ganache: Place chocolate in a medium heat-proof bowl. Set aside. In a small saucepan over medium heat, bring cream just to a boil. Immediately pour cream over chocolate and let sit without stirring for one minute. Then, whisk mixture gently until completely melted. Add hazelnut spread and rum, if using, and whisk until completely smooth. If mixture is warm, allow to cool slightly. Divide evenly between serving cups on top of the mousse. Garnish with coarsely chopped hazelnuts.
Place mousse in the refrigerator to set for at least 2 hours.
Keep mousse in the fridge, covered with plastic wrap, for up to 3 days.