Heat the olive oil in a non-stick frying pan. Fry the mushrooms for approx. 3 mins. Reduce the heat, dust with flour, fry for a little longer and remove. Add a little oil if necessary, stir fry the carrots and leeks for approx. 3 mins. Add the tomatoes, pour in the water, bring to the boil. Reduce the heat, return the mushrooms to the pan, cover and simmer the vegetables for approx. 10 mins. until almost soft. Shortly before serving, stir in the olives and sage, season.
Bring the water and milk to the boil in a pan, season with salt. Stir in the cornmeal. Reduce the heat, simmer for approx. 5 mins. over a very low heat, stirring continuously to form a paste. Heat 1/2 tbsp of olive oil in a non-stick frying pan and reduce the heat slightly. Add the polenta and fry over a medium heat for approx. 10 mins. Place a flat plate over the pan, tip the polenta onto the plate. Add a little olive oil to the pan if necessary. Slide the polenta back into the pan and cook for approx. 10 mins.