Preheat oven to 350 degrees F. Line muffin tin with paper cupcake liners.
Cream the butter and sugar at medium speed, then reduce to low. Add the eggs one at a time, then add the vanilla extract.
Sift together the flour, baking powder, and salt. Mix together with ground hazelnuts.
While mixing on low, add 1/3 of the flour mixture to the bowl, then the milk, then another 1/3. Add the Nocciolata before the rest of the dry ingredients.
Scoop batter into lined muffin tins with an ice cream scoop. Bake about 18 minutes, rotating pans halfway through.
Cool for 5 minutes before removing from pan, then move to racks to cool completely.
For frosting: Beat the butter and Nocciolata until smooth and add the vanilla extract. Slowly add the powdered sugar, then the milk. Add a little more milk if frosting is too thick or not smooth. Add more powdered sugar if the frosting is too runny.
Frost the cupcakes once they reach room temperature. Top with a whole hazelnut, if you so desire!