In a bowl, divide the egg yolks from the whites. Add the sugar, the melted butter, and the milk to the yolks. Stir all the ingredients until well combined;
Add the flour with the baking powder and 1 cup of chopped hazelnuts to the batter (save the rest for the final decoration). If you only have whole hazelnuts, pulse them with 1/4 cup of sugar in a food processor;
Add the chocolate chips and mix well;
Whip the whites to a stiff peak with a hand mixer at high speed;
Fold the whites into the batter to maintain as much volume as possible;
Pour the batter into a buttered and floured cake pan or parchment-lined pan;
Sprinkle the surface of the cake with the remaining chopped hazelnuts for a delicious crunchy top crust;
Preheat the oven to 350°F (180°C) and bake for 40 minutes in a static oven;
Check the surface; if the top gets too brown, lower the temperature;
Do the toothpick test; insert one into the cake, and if it comes out clean, it is ready. If after 40 minutes, the cake is not done, raise the temperature to 430°F (about 220°C) and bake for up to 10 minutes more but keep the oven door slightly open to remove the moisture;
Once cool, sprinkle it with powdered sugar. Your hazelnut cake is ready! Enjoy!