Make a yeast dough with alittle lukewarm milk, 1tablespoon granulated sugar and the yeast. Let this starter mixture rest for 10 minutes.
Mix 3 egg yolks and the egg white with the starter mixture. Add the rest of the milk and granulated sugar and the salt. Mix with the flour.
Little by little work in half of the butter. Knead the dough on a floured board for about 15 minutes. Let the dough rest till it doubles in bulk. Preheat oven to 350°F.
Butter metal baking tubes ½inch in diameter and about 6inches long. Roll dough to a thin sheet and cut strips 8inches long and ½inch wide.
Roll the strips in spirals on the buttered tubes. Make as many as the dough allows. Let them rest for 10 minutes. During this rest butter the dough twice, using a brush. Beat the whole egg with 1teaspoon water. Finally brush the dough spirals with this egg wash.
Roll the spirals in the chopped walnuts and bake in the preheated oven for about 15 minutes.
Gently pull off the cakes from the tubes and sprinkle them with vanilla sugar. Serve the cakes while hot, with jam.