Preheat the oven to 160ºC/325ºF/gas 3. Rub a 20cm springform cake tin with olive oil, then line the base with greaseproof paper and rub the paper with oil, too.
Squeeze the juice of 3 oranges (roughly 100ml) into a pan, add 100g of honey and simmer until thickened and reduced, then remove from the heat.
Meanwhile, in a free-standing mixer on a high speed, whisk 200ml of olive oil with the remaining 150g of honey for 2 minutes to combine.
Beat in the eggs for 2 minutes, while you finely grate and add the zest of 3 oranges.
Stop the mixer, then fold in the ground almonds, polenta, and the juice of 1 or 2 oranges (roughly 50ml).
Pour into the prepared tin and bake for 40 to 50 minutes, or until golden and cooked through. Leave to cool for 10 minutes in the tin, loosening with a palette knife before releasing – be gentle with it.
To serve, quickly peel and slice the remaining oranges and dish up alongside the cake, drizzling the pretty syrup over everything before tucking in.