Heat the oil over a medium high heat. Add the onion and carrot and cook for a couple of minutes then add the garlic, courgette and mushrooms. Cook for another 5-10 minutes until everything is softened then add the chopped tomatoes, red wine and thyme and bring to a simmer. Cook for 15-20 minutes until the sauce has thickened.
Bring the milk and vegetable stock to a boil and slowly pour in the polenta whisking constantly. Lower the heat and cook for 10 minutes then add the butter and cheddar and stir until melted. Serve the polenta topped with the stew.
Nutrition information is an estimate and will vary depending on the ingredients used.