Preheat oven to 350°F. Grease or line a 9-inch cake pan.
In a medium bowl, whisk together the flour, baking powder, and salt.
In a large bowl, beat the butter and sugar together until light and fluffy. Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Add the flour mixture to the butter mixture, alternating with the milk, beginning and ending with the flour mixture. Mix until just combined.
Fold in the chopped chocolate and hazelnuts.
Pour the batter into the prepared pan and smooth the top with a spatula.
Bake for 35-40 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 10 minutes, then remove it from the pan and let it cool completely on a wire rack.
