Work flour, butter, vanilla sugar and lemon peel to a shortcrust and let it chill in the refrigerator for about 1 hour. Dice the candied fruit into fine pieces, douse with the port wine and then let soak for about an hour.
Boil the rice with the sugar in milk and add a pinch of salt till it has soaked up the liquid and softened. Let cool.
Separate the egg yolks from whites. Beat the remaining butter, egg yolks, sugar, vanilla sugar and rum until fluffy. Bit by bit, add in the cooled rice and candied fruit. Beat the egg whites and carefully fold into the rice mixture.
Roll the shortcrust out on a baking sheet, and place in the bottom of a springform pan. Create a crust of one inches along the rim of the baking form.
Spread the apricot jam evenly on the shortcrust and add the rice mixture to the form.
Bake in a preheated 430 degrees F oven for about 25 minutes.
When the cake is cool, sprinkle it with powder sugar.