Place the melted butter in a mixing bowl. Add the sugar and whisk until the mixture turns white.
Add the eggs one at a time, stirring constantly.
Next, add the salt, vanilla extract, flour, ground hazelnuts, and baking powder, stirring with a spatula.
Pour the batter into a buttered and floured cake pan and bake in the oven for 45 minutes at 350°F (180°C).
Once out of the oven, wait 5 minutes before turning the pound cake out onto a wire rack using a tea towel to avoid burning yourself. Then leave it to cool.