Preheat the oven to 165°C (conventional oven, not fan).
Place the caster sugar into the bowl of an electric stand mixer, fitted with the whisk attachment. Zest all 4 oranges directly into the bowl with the sugar, then use the back of spoon to press the zest into the sugar until evenly distributed.
Add the eggs to the sugar, then whisk on high speed until the mixture has become pale and doubled in size. It should be thick and creamy, like the consistency of softly whipped cream.
While the egg mixture is whisking, combine the flour, baking powder and sea salt in a mixing bowl. Set aside.
With the mixer running, pour the olive oil into the egg mixture in a slow, steady stream, until it is all incorporated.
Repeat this process with the orange juice, pouring it in in a slow, steady stream with the mixer running, until it is all incorporated.
Remove the bowl from the stand mixer and sift 1/4 of the dry ingredient mixture directly over the surface of the batter. Use a handheld balloon whisk to fold the dry ingredients in gently, but thoroughly.
Repeat this process 3 more times, adding 1/4 of the dry ingredients each time, until they are completely incorporated. Switch to a spatula for one final, brief stir to make sure no flour remains at the bottom of the bowl.
Divide the batter between the two prepared tins, then bake in the preheated oven for 35-40 minutes, until the edges of the cakes are starting to pull away from the sides of the tins and a skewer inserted into the centre of the cakes comes out clean.
As soon as the cakes come out of the oven, use your fingers, or the flat edge of a palette knife, to very gently push the edges of the cakes inwards, towards the centre. This helps the cakes to release from the sides of the tin, making it easier to get them out of the tin once they are cool and ensuring that the cakes have neat edges later.
Allow the cakes to cool most of the way in the tin, then turn out onto a wire rack, carefully remove the baking paper from the bottom and allow to cool completely before assembling.