Boil 3 1/3 cups (800 ml) of the milk with half the sugar. Beat the eggs with the remaining sugar, add the vanilla and rum. In another container, dissolve the flour with the remaining milk. Add them to the eggs, stir well and add to the boiling milk, while stirring energetically.
Once the cream thickens, take it off the stove. Cut the cozonac into pieces about 1/2″ (1 cm) thick. Let the coffee cool and add the sugar to it. Dip the pieces of cozonac in the coffee and arrange them in a form with removable sides.
Pour in 1/3 of the hot cream. Arrange a 2nd layer of cozonac, pour in another layer of cream and cover with a 3rd layer of cozonac. Finish off with cream and leave the cake in the fridge at least overnight. Sprinkle with cocoa and serve!