Preheat the oven to 180C/350F/gas mark 4 and grease a deep, 23cm round cake tin and line the base with baking parchment.
Using an electric mixer, whisk together the eggs and sugars until thick and pale then whisk in the vanilla extract. Mix together the flour, baking powder and cocoa powder then sift it into the egg mixture.
Begin to fold in the flour until the mixture starts to look gungy then add the olive oil, milk, rosemary and salt. Continue to fold everything together until smooth.
Pour the batter into the prepared tin and bake for 30-40 minutes, until a skewer inserted into the centre comes out with moist crumbs but no wet batter; if it comes out clean then the cake is overdone.
Poke a few holes in the top of the cake with a skewer then brush very generously with some of the reserved syrup (at least 4tbsp worth); leave to cool in the tin for 10 minutes then turn out onto a wire rack and leave to cool completely. You can give the cake another brushing of syrup if you like.
Once the cake is cool, transfer it to a serving platter and arrange the orange slices on top, drizzle with a little more syrup and serve.