Preheat oven to 350 F.
Grease and line an 9 x 5 inch loaf pan with parchment paper. If you prefer to make a round cake, rather than a loaf, you can use a 9-inch springform pan.
In a food processor, combine hazelnuts, butter, and sugar. Pulse until a smooth paste of ground hazelnuts, sugar, and butter forms.
Add the eggs to the ground nuts and butter mixture, processing to combine after each egg is added.
Add the vanilla and the milk, scraping down the sides if needed.
Add the flour and salt, processing until the flour mixture is just combined with the batter.
Bake for 60 minutes in preheated oven until the top of the cake is golden brown and a cake tester inserted into the center of the loaf comes out clean.
Remove cake from oven and let cool for 10 minutes, before removing the cake from the loaf pan. Let cake cool on a wire rack until the cake is at room temperature.