Preheat oven to 180°C/350°F/Gas Mark 4. Line a 23–25 cm (9–10 in) springform cake tin with baking paper. Wipe oranges well and place in a deep saucepan with enough cold water to cover. Bring to the boil and cook with the lid on for 20 minutes. Remove from the pan and cool for 20 minutes. Cut in half and remove any seeds, then place in a food processor, skin and all. Add caster sugar and process for 30 seconds. Add almonds, eggs, baking powder and half the rosewater and purée for 10 seconds. Scrape down the sides of the bowl and purée for a further 10 seconds. Pour the mixture into the tin and bake 60 minutes. Check after 50 minutes by inserting a skewer into the centre of the cake. It should come out slightly moist, but if you think it needs more cooking, cover the tin with foil and cook until done.
Cool for 30 minutes in the tin before removing and placing on a plate. Meanwhile, bring orange juice, zest and sugar to the boil, simmer until syrupy, then remove from the heat and add remaining rosewater. Prick the top of the cake 20 times with a skewer and spoon the syrup over.