Soak the orange rinds in the rum.
Put the washed and strained rice to boil in water for 2 min. Separately, bring the milk to a boil and add the sugar, vanilla and strained semi-boiled rice to it.
Beat the egg whites to hard snow and mix them carefully with the rice mixture.
Caramelize the sugar in a cake form or tray by mixing it with the lemon juice and a teaspoon of water. Let it cool and distribute the rice on top.
Put the oven dish in a water bath and place it in a moderately heated oven for 30-40 min. to bake. Invert the Pirincli Tatlu cake onto a platter and serve.