Heat the oven to 170C.

Grease a 6" cake pan, and line the bottom with parchment

In a bowl, beat the sugar and softened butter together.

Add the yolks one by one to the butter and sugar mixture, taking care to mix each one thoroughly before adding the next one and beat until you obtain a smooth batter.

Add the rhum and the orange essence/Cointreau and mix again.

Mix the flour and baking powder together and add it to the batter by "raining it in". Mix well.

Cut and juice the oranges. Pour half of the resulting juice in the batter, add the zest and mix.

Beat the whites until firm with the pinch of salt. Add them delicately to the batter.

Pour the batter into the pan and bake for an hour, checking the coloration from time to time. It will be dark orange when done.

Pour the other half of the juice into the cake while it's still warm. Take care not to pour it too fast and not to let the cake cool too much before you do so. You may find that if you don't get the timing right, your whole cake will not have juice in it (as in it may have two different textures and have a visible line halfway down where the juice stopped penetrating).