First prepare the oranges. Wash them, cut them into slices half a centimetre thick and remove any seeds. Put a large frying pan on the stove with the water and sugar; when it begins to boil, lay the slices of orange in the syrup, put the lid on the pan and simmer for 10 minutes, until they become shiny and soft. If you use star anise, add the pods 3 minutes before the end of the cooking time. Carefully remove the slices of orange and lay them on a sheet of greaseproof paper. In a large bowl, mix the softened butter (taken out of the fridge at least half an hour beforehand) with the sugar. In another bowl, mix the sifted flour and baking powder with the grated lemon peel. First stir one egg into the butter and sugar mixture and then, when it is completely incorporated, add ⅓ of the flour mixture and ⅓ of the milk, to which you have added the vanilla extract. When everything is amalgamated, add another egg, another ⅓ of the flour and of the milk; then do the same with the last egg and the remaining flour and milk. Mix thoroughly until smooth and homogenous. Arrange the slices of orange in concentric circles, overlapping them slightly, in the bottom of a 26 cm round springform cake tin which you have greased well with butter and dusted lightly with flour. Pour in the cake batter, level the surface and bake in a preheated oven, at 180 °C, for approximately 35-40 minutes. When this time is up, do the “toothpick test”: stick it into the centre and if it comes out dry the cake is cooked. Leave it to cool down completely and then remove the ring from the springform tin. Turn the cake over onto a serving dish, remove the base of the tin as well and now... your upside-down cake is ready to be eaten!