For the almond nut croissants, heat the milk to lukewarm. Crumble in the yeast and stir to dissolve. Put the flour in a large enough bowl, add the milk with the yeast, eggs, fat and sugar and knead everything together. Cover and let rise in a warm place for about an hour.
In the meantime, chop the hazelnuts and almond kernels for the filling. Boil the water and sugar in a saucepan to a thick syrup. Fold in the chopped nuts and almond kernels and let cool.
Divide the yeast dough into two portions, roll out into 35 cm circles. Whip the egg whites until stiff, fold into the nut mixture, spread onto the circles.
Cut each dough circle into eight pie pieces, roll each piece up from the wide side to the tip. Shape the pieces into croissants and place, seam side down, on two baking sheets lined with parchment paper. Cover and let rise for about 20 minutes.
Heat the oven to 225 °C. Mix the egg yolks and brush the croissants with the mixture. Place the baking trays one after the other on the middle shelf in the oven and bake the almond nut croissants for about 10 minutes.