Boil 600 ml milk. Let the rice swell in it at low heat for about 40 minutes. Season to taste with 4 tablespoons of sugar and cinnamon. Let the rice cool down
Melt the fat. Heat up 100 ml milk. Dissolve yeast in it. Add fat, 1 tbsp. sugar and yeast milk to the flour and knead until smooth. Cover and leave to rise in a warm place for about 30 minutes
Knead the dough again and roll out to a circle (approx. 26 cm Ø) on a little flour. Place in a greased pizza, pie or springform pan (24-26 cm Ø). Press on the edge. Leave to rise for about 10 minutes
Separate eggs. Beat egg whites until stiff, add vanilla sugar. Fold the beaten egg whites into 1/4 rice pudding. Mix the rest of the rice with the egg yolk, spread on the dough. Spread the beaten egg white rice on top. Bake the rice cakes on the 2nd rack from below in a hot oven (electric range: 200 °C/ convection oven: 175 °C / gas: level 3) for 25-30 minutes. Sprinkle with sugar crystals if necessary