Put the dried mushrooms in a heatproof bowl and cover with boiling water. Leave to soak while you prepare the rice.
Heat the olive oil in a heavy-based saucepan, add the rice and stir well to coat the grains with the oil. Add the hot stock and bring to the boil. Reduce the heat, partially cover and simmer, stirring frequently, for 12–15 minutes until the rice is tender and all the stock has been absorbed. Transfer to a bowl.
Meanwhile, melt the butter in a saucepan, add the onion and garlic and cook gently for 5 minutes.
Drain and chop the soaked mushrooms, then add to the rice with the onion mixture, chestnuts, Parmesan and egg. Stir until well combined and season to taste with salt and pepper.
Divide the mixture into 12 portions. Pat each portion into a cake and roll in the polenta. Heat a shallow depth of vegetable oil in a frying pan, add the cakes and cook for 2 minutes on each side until golden. Garnish each serving with a lemon wedge and serve immediately with mixed salad leaves.