For the hazelnut cake: Preheat the oven to 325 degrees F. Butter and flour a 9-inch round or square baking pan.
Pulse the hazelnuts until coarsely chopped in a food processor. Reserve. Combine the flour, cocoa powder, baking powder and salt together in a medium bowl.
Combine the butter, sugar and vanilla in a large mixing bowl, and then beat until the mixture is light and fluffy, using an electric mixer. Beat in the eggs one at a time. Add the hazelnut paste and beat until incorporated and there are no lumps. Gradually add in the flour mixture, stopping the beater when it is just combined.
Fold 1 cup of the chopped hazelnuts into the batter, reserving the rest for garnish.
Transfer the batter to the pan and bake until a toothpick comes out clean when inserted into the middle of the cake, 45 to 50 minutes. Let the cake cool 10 minutes, then remove from the pan and let cool completely.
For the nutella mousse: Mix the Nutella and mascarpone in a large bowl to combine. Beat the heavy cream in another large bowl, using a hand mixer, until just under soft peaks. Add in the Nutella mixture in 2 additions, and beat until you don't see any streaks. Place the mousse in a pastry bag fitted with a medium star tip. Refrigerate until ready to serve.
To serve and assemble the cake: Cut the cake into 3-inch squares or rounds and cut each in half equatorially. Pipe the mousse on both the bottom and top halves of each of the cakes, and then give each cake a light sprinkey-dink of the chopped hazelnuts.
Recipe adapted from Anne Burrell, Cook Like a Rock Star