Roll the whole orange and lemon over the countertop under your palms, until softened. Place both in a large, heavy-bottomed saucepan and cover with water to at least 2 inches above. Cut a circle of greaseproof paper to fit the pot and place over the water, then put on the lid. Bring to the boil, then reduce the heat to very low – ideally, move the pot to the smallest ring on the lowest setting – and simmer for 40 minutes. (The paper circle will help to keep the fruit submerged whilst simmering).
Preheat oven to 180 C / 160 C Fan / Gas 4. Lightly grease the bottom and sides of a 23cm diameter springform cake tin with oil and cover the bottom with parchment, ensuring the circle is large enough to cover the join of the ring. Very lightly grease the top of the parchment.
Carefully remove the boiled orange and lemon from the pot, slice each into quarters, and remove all seeds. Slice each quartered fruit 3 times, then add the boiled fruit pieces – peel ‘n all – with the orange and lemon juice and pulp to a food processor, or heavy-duty blender. Whizz until it's completely, thoroughly combined, no pieces of peel are evident, and it's very thick; about 2 minutes.
In a large bowl, whisk the eggs and sugar until foamy. Add the whizzed fruit, almonds and oil, and continue whisking at medium-high speed until fully combined, about 2 minutes.
In a small bowl, mix the polenta, baking powder and spices together with a fork. Add this to the wet ingredients, and fold gently with a spatula or large spoon until fully combined.
Pour the cake mixture into your prepared tin and bake for 45 to 50 minutes, turning the tin halfway through for even baking. When a skewer inserted into the centre comes out clean, turn off the oven and remove the cake from the oven to a cooling rack. Unclip the ring and slide off the tin's base after about 20 minutes – this will help the cake cool faster.
Spread the reserved orange zest on an oven-safe plate, breaking up any clumps, and leave in the oven – door ajar – to dry out as the oven cools.
Sift the icing sugar into a medium bowl, and manually stir in the reserved lemon zest, vanilla, spices and 3 tablespoons of the orange juice, quite vigorously, until smooth. Use your own judgment on how thick/thin you want it – add 1 tablespoon or more orange juice to make it looser. Place the icing bowl in the fridge until the cake has cooled.
When the cake has fully cooled, remove the parchment, and transfer the cake to a serving plate. Give the icing a really good stir, and spread the icing over the cake. (If the cake is even slightly warm, the icing will melt and thin out.)
Add a large pinch or two of caster sugar to the dried orange zest, and mix with your fingers until all strands are fully coated. Sprinkle over the cake to garnish. Put the cake in the fridge until ready to serve.
For a syrup topping...
Instead of icing, you can opt for a syrup topping: Whilst the cake is baking, heat the juice of 3 large oranges with 75g caster sugar and the reserved lemon zest to the boil on the hob in a small saucepan. Reduce the heat to the very lowest setting, and keep stirring until the mixture thickens into syrup. (You can let this cool, then re-heat when the cake is almost baked.) Treat this like lemon drizzle: i.e., when the cake is out of the oven, poke it deeply all over with a skewer, and pour the syrup over the top so it soaks in. If doing this, I’d still dry the remaining orange zest in the oven as it cools, and coat it with caster sugar to use as a topping – for visual wow, and extra citrus flavour.