Put the whole oranges in a pan, cover with water and boil, covered, for 1 hr until a knife easily pierces them. If the oranges won’t stay under the water, place a small saucepan lid directly on top to keep them submerged. Remove the oranges from the water and cool, then quarter and remove any seeds and obvious pith where the stalk was. Blitz the oranges to a rough purée with a hand blender or in a food processor and put in a large bowl.
Heat oven to 160C/140C fan/gas 3 and line the base and sides of a 21cm loose-bottomed cake tin with baking parchment. Beat the cardamom, xylitol and eggs into the orange purée, then mix the ground almonds with the polenta, flour and baking powder, and fold in until well blended. Scrape the mixture into the tin, level the top and bake for 40 mins.
After 40 minutes, scatter over the almonds, quickly return to the oven and bake 20-25 mins more until a skewer inserted into the centre comes out clean. Remove from the tin and leave to cool. Serve sliced as a cake, or with Greek yogurt or cream as a dessert.