Preheat oven to 160°C (140°C fan-forced).
Grease and line a 12 cm x 20 cm loaf tin, or a round 24 cm diameter springform cake tin.
Place the oranges in a saucepan, cover with water, bring to the boil, then turn down to a simmer and cook for about 20 minutes.
Grind all the nuts together in a food processor or blender.
Once the oranges are cooked, drain the water, then chop them up, discard seeds and puree the oranges in a food processor.
Whisk the eggs and sugar together in an electric mixer until pale and fluffy.
Turn the mixer down to its lowest speed and add the orange puree and olive oil, then the ground nuts, flour, grated ginger and a pinch of salt.
Pour the mixture into the prepared tin, smooth out the top, then bake for 1 - 1 1/4 hours until golden and an inserted skewer comes out clean. Allow the the cake to cool before turning it out onto a wire rack.
Drizzle with orange ginger syrup and serve with any remaining orange puree, cream or coconut yoghurt, or serve it just as it is.