Cook the rice in about 350 cl.boiling milk and 50 g sugar. Prepare the cream in another pan by bringing 750 cl milk to the boil with the lemon peel and the vanillin. In the meantime, work the eggs with the sugar and then add the flour. Pour in the hot milk and stir, bring to the boil and then cook the cream slowly for a few minutes. Add the cooked rice and stir. Butter and flour a baking tin and line with the short pastry. Pour in the cream and put into the oven which was preheated at 180° for about 35 minutes. Remove from the oven and serve hot, perhaps accompanied by a spoonful of vanilla cream.